Everything is different, and I would recommend none of them to a class player.
Sicilian defense

Their main difference is that theory ends around move 30 for 6.Be3, while for 6.Bg5 it ends around move 40.
A class player like you should not care at all about theoretical lines going over move six. So...

Thank you. You're right, I'm not interested or capable of learning that much theory. I just wanted to know, if there was one, the basic difference in plans. This seems to be a much too difficult question to explain to a 1900 player I suppose.

It's not so difficult to explain the differences, but it's much easier to say to you that a non-pro player should not care about such very complex and over-analysed lines.
A 1900 player may indeed start wondering about the differences and fine details behind Bg5 and Be3. But I'm talking about 1900 FIDE- neither USCF, nor chess.com

I was talking about 1900 USCF which I realize is about 200 points greater than the equivalent FIDE rating. Thanks for your help pfren.

I was talking about 1900 USCF which I realize is about 200 points greater than the equivalent FIDE rating. Thanks for your help pfren.
I don't think that the difference is that great, around 110-130 points would be more accurate. Anyway, regardless of the actual player strength, if you want to learn these two lines really well, you must dedicate a lot of time- and I mean A LOT. Better play something less critical, but easier/lazier to master.

No, but they should stick to something simple to master. True, almost all the reliable Sicilian variations have a respectable amount of theory, but they aren't all "the same".

Yes, not so much theory, and while the mainlines are "equal" there is quite some play left for both sides.

Their main difference is that theory ends around move 30 for 6.Be3, while for 6.Bg5 it ends around move 40.
A class player like you should not care at all about theoretical lines going over move six. So...
Oh, are you jealous that people with a life outside of chess play the cool lines? Would you like them to be reserved only to you and your "elite"?
Let me tell you what. If GMs know the 6.Bg5 theory until move 40 this has absolutely no relevance to us class players. If a line has complicated theory we just need to know as much theory as our opponent. So if a 1700 knows, let's say, theory until move 15 (understanding it, not just memorized) he's not going to be outbooked by another 1700.
And studying theory of complicated stuff (with moderation) is the best way to improve the positional understanding.

I would recommend the closed sicilian, Boris Spassky played this more than probably any other World Champ and had good success with it. In my opinion the Alapin is very dry(many players love it though, give it a shot to see what you think). Here's a line I would suggest trying as well:

Oh, are you jealous that people with a life outside of chess play the cool lines? Would you like them to be reserved only to you and your "elite"?
Let me tell you what. If GMs know the 6.Bg5 theory until move 40 this has absolutely no relevance to us class players. If a line has complicated theory we just need to know as much theory as our opponent. So if a 1700 knows, let's say, theory until move 15 (understanding it, not just memorized) he's not going to be outbooked by another 1700.
And studying theory of complicated stuff (with moderation) is the best way to improve the positional understanding.
I might have the chance to intoduce you to an IM who hardly knows any opening theory. Sometimes he got crushed in a few moves because he ignored existing traps- yet he had reached at a time a rating around 2440 by playing stuff like 1.e4 e5 2.Nf3 Qe7 and such.
May I kindly ask what YOUR rating is and how much studying opening theory had benefited you? Take your time...
For the record, you remind me of one of my best OTB "clients". He is always booked/armed with the latest opening trend and GM novelty. He has scored against me half a point in nine games, and the recipe was always the same: I played complete nonsense in the opening, borderline not losing by force, yet complex and non-book. Most of the games ended in less than 25 moves. He is a FIDE titled player, yet he plays badly- it's just that his opponents do not apply the correct recipe.
Do you really envy such players?

@ pfren: I agree with your posts. I have a question though:
Given the highly theoretical nature of some chess openings, such as the Najdorf, would it be better for class players to just not play those openings at all? If a class player wants to play the Najdorf as Black anyways, do you recommend memorizing the main lines (or as much of it as the player can do) or to just play some offbeat stuff to avoid the main lines and to avoid having to memorize, as you said, 30 moves?

You can find some semi-correct sideline to play... but entering stuff like the Poisoned Pawn, where endless sheets of mixed human and computer generated crap is widely available, sometimes exceeding move 50, makes no sense at all for a class player. Same goes for mainline Dragon, as well as other openings, e.g. the Ruy Marshall. Even if you manage to absorb all that crap, it's not nice polaying against a woodpusher who just happens to eat books for breakfast, and draw or lose against him, while you could have a very easy life against him using 1.e4 h6.
I would suggest (for Black) to class players either the Kan or the Sveshnikov- the former is mainly a matter of sane positional play, while the latter is quite theory-heavy but easy to understand, and it will also help you improve your positional understanding (at least it will teach you that offering your opponent d5 on a plate, or leaving the d6 pawn permanently weak aren't the end of the world, if they are dynamically compensated).
What's the main difference in plans for white in the Be3 (English attack) and Bg5 variations of the Sicilian? Which would you recommend for white?