First, let's differentiate between bellydance and Middle Eastern dance. Many styles of bellydance, but not all, are Middle Eastern dance, and a fair few styles of Middle Eastern dance are bellydance, but far from the majority. Nadira has a wonderful diagram that makes more sense of in a smaller space than my rambling about it will. It's also worth noting that in order to talk about one style or another, you HAVE to talk about the time period you're referring to. Differentiating between Turkish and Egyptian style, at least as enjoyed by the upper classes, would be useless if you're looking during the Ottoman empire when fashionable entertainment was Turkish. But during the 1960's, for example, the two countries had very different styles.
Also, remember that there is no value judgement in differentiating styles. I advocate doing it so we can appreciate each style's unique contributions and beauty, not in order to berate anyone into a mold.
It's a good idea to learn to do more than one style, but there's a lot of them! At the very least we should all learn about all the different manifestations of bellydance. Now, down to the reasons why it's worth it!
For fun! If you're reading this then, like me, you probably have a knack for curiosity, and learning about the nuances and history of different styles can give your curiosity beast a bone to chew on.
To make sense of things: knowing the characteristics of different styles can help you understand why one teacher tells you to do things one way, and another tells you something totally contradictory. Of course there is plenty of variation within a style, but some contractions are too extreme to reconcile without putting them in context.
To study what you like: just like knowing what kind of food you like: if you want fajitas but don't know the difference between Tex-Mex and authentic Mexican food you'll be disappointed at an authentic restaurant. Likewise if you want to learn Turkish style and sign up for a workshop with an Egyptian instructor the content of the class won't satisfy you the same way. No matter how good the workshop is.
To watch a wider variety: This is especially important for newer dancers to learn, because Youtube "knows" the styles, and the suggested videos are usually the same style. If you start watching vintage Turkish the suggested videos will be more vintage Turkish. If you start watching modern Egyptian the suggested videos will be more modern Egyptian. start with tribal, more tribal suggestions. If you don't know the different styles yourself, it is hard to realize that you're being limited this way, making it harder to break out of that rut and narrowing the spectrum of dance that you get exposed to. It's as if there's a whole beautiful rainbow of colors out there but you's only experienced the world in shades of red. But, if you know the styles, you can recognize the trend, and add variety by whenever you want.
For expression: You'll want to pick the best medium to express what you want to say. For example, tarab and shaabi have very different feelings and are suited to saying very different things to your audience.
To provide appropriate performances at different venues. In this vein, knowing my way around the different types of styles helps me know better than to do tarab, or obscure folk styles at my restaurant gig. An audience at a hooka bar doesn't want to see deep emotional or theatrical pieces. A wedding intending to celebrate the bride's Turkish heritage isn't looking for an Egyptian type of performance. This is also something to be said for knowing your song lyrics here: even if your clients want an emotional performance it's important to steer clear of songs of unfaithful lovers when performing for newly-weds ^_~
To better suss out what your client wants. Everyone has associations attached to the words they use, and most of us assume that others share the same perspective. For example, the word "dame" in Spanish means "give me" whereas in Japanese it means "stop it, that's bad, don't do it". Imagine you're a Japanese speaker and a Spanish speaker is offering you a bowl of food that you're allergic to. You tell them "dame" meaning "I can't have it" and they thrust the food over to you, thinking you are asking it to be passed to you! Now imagine that a Lebanese client calls up and asks you to include a cane number in your set. Having been trained in the context of Egyptian folk dances you assume they must mean Saidi, after all a beledi cane would be a little low-key for their event. The day comes and you can't understand where their enthusiasm went. It would be as if they thought they were getting mozzarella cheese and weren't prepared for the flavor of brie. We've all been there.
Figuring out what a client wants is always hard, but having an idea of their assumptions and associations they're coming to the conversation with can help you pick your costume, music, set components, and even movement and emotive style.
Both of these points contribute to a third practical reason: to not embarrass yourself! In addition to the reasons mentioned above, if you don't know the difference it's easy to dance a Romani song in the style of Egyptian Tarab, with results just as embarrassing as if you danced the waltz to a Salsa song, wrong steps for the time signature and all.
Socially Conscientious Reasons
For context. As mentioned above some things seem to contradict each other, and realizing they don't belong to the same style can reconcile this. I'm bringing it up again here because I'm reminded of an anecdote from Sahra Saeeda's early research days. She related, on Nadira's clubhouse Podcast, how when she was still learning about Egyptian dance she heard a piece of information about Saidi style of dance and related it to her friend, Farida Fahmy. Farida asked where she had heard it and Sahra said "from an Egyptian". Farida pressed, "Is he Saidi? Does he own a farm or work in the government?", that is, what sort of social class and circle does he belong to, what kind of experience does he have with the subject matter he is informing on. Turns out the gentleman was from Cairo and Farida said "you just learned what a Cairo person thinks of Saidi dance". If we lump everything together as in "all of this- beledi, shaabi, Saidi, ghawazee, fellahi, Nubian, orientale, Siwa, bamboutayya, marhaganaat- is Egyptian" (or further still, if we we group Romani, Lebanese oriental, khalegy, shaabi- as one thing called Oriental dance) then we're bound to be that girl who does the bellydance equivalent of dancing ballet to a Tupac song (after all, it's all Western stuff). Each of these kinds of dance has a different social and cultural context. To entertain clients, in the case of ghawazee or orientale dancers. To entertain one's self or one's friends, in the case of folk dances. This goes on.
Learning different styles is an exercise in seeing dance on the terms of the country it comes from. As mentioned above everyone has their own assumptions and associations with the term "bellydance". We tend to come to this dance with a sort of "home style", as in a baseline that we compare the rest of what we see to. I remember watching some Modern American dancers with another dancer who "grew up" in the Vintage American style. (During the 80s and 90s the trend in the US shifted from a heavy Turkish influence to a taste for Egyptian, but dancers still had to tailor their performances to American audiences, and we all tend to dance with a bit of an accent of our own culture.) She commented that we'd watched a lot of Egyptian style. I was confused, being in the habit of comparing things to Fifi Abdou, Souheir Zeki, Samia Gamal, and Naima Akef these performances seemed very American to me. For her; being in the habit of comparing things to a mix of Tulay Karaca, Birgül Beray, Princess Banu, and Serena Wilson and Helena Vlahos; they seemed very Egyptian.
Later we watched a contemporary American dancer who followed a more Turkish styling, and my friend could immediately recognize the American accent in her dancing, which was lost on me. Understanding what elements of the dance apply to each style helps us to see the dance on the terms of the culture it belongs to.
It opens your acceptance of a wider variety of expressions. Many seem to think differentiating between the many styles of bellydance puts up walls and boxes people in. But I think it does just the opposite. It's easy, if your only experience with bellydance is, for example, Modern Egyptian style to turn up your nose at even the most well done Romani piece. In fact, if Modern Egyptian was your only experience then even a golden era Egyptian style performance would seem sloppy.
I've heard some dancers say that "it's all bellydance and we shouldn't be boxing it up" in one breath, but then turn around and denigrate another style of dancers for doing things differently than what she was used to in the next breath. Understanding the characteristics of as many styles as possible gives us context and allows us to see the validity of different performances. Not only will you have the opportunity to enjoy a wider range of performances, but knowing about the context and components of different styles lets you appreciate them on their terms.
That dreaded discussion
This does lead us into the question of "when does it change so much that it ceases to be bellydance?" that we sought to avoid at the beginning of this post. I hope both sides can see why each other gets defensive when the subject comes up. For dancers advocating to keep calling newer fusions (such as the modern competition style so shaped by the Russian ballerinas, ballroom-esque competitions, and audiences of judges instead of party guests) bellydance, the idea that this style is no longer part of the bellydance family of styles threatens their identity as bellydancers. For dancers brought up in the older styles, so focused on improvisation, grooving on the music and weaving an intoxicating magic around the audience, the idea that something could still be bellydance without the aspects most responsible for their emotional connection hollows out the meaning of an art form very dear to them.
While I wouldn't consider this modern style Middle Eastern bellydance, I do think there is still room for it to be bellydance. This style might be considered on the fringe of what is bellydance, when we take into account everything that makes a dance what it is: the dancer's relationship to the music, audience, technique, center of gravity, use of space, etc. I've seen the same performers (no names!) straddle this gap, with some pieces that might fall into modern bellydance and others falling into something of a burlesque-pop and lock fusion in a bellydance costume.
At the same time, I don't agree that these sorts of new styles popping up are bound to be the end of bellydance. I don't think this dance could have survived for hundreds, if not thousands, of years to be done-in by "these young whippersnappers". I believe there is enough in the core of bellydance that it -in all of it's incarnations- will find someone to speak to, sooth, excite, and enchant; and someone to carry it forward.