I play all 3 Real Bout games, and I'd have to say Real Bout Fatal Fury 2 is my favorite just because of it's speed and how nicely it controls.
Real Bout 1 is good hilarious fun, ring outs are pretty dumb, but they make the game way more intense. Of the three Real Bout games, RB1 had the most stupid version of Kim, Blue Mary was also really insane in this game, and Franco was pretty much the ring out King. I really hate the way the background/foreground works in this game, it's way too slow, and you're completely defenseless to boot. If you knock the opponent into the background/foreground, you can punish them super hard for it, often leading to easy ring outs.
Real Bout Special is great with it's character variet, although having a non-playable/banned Geese sucks alot. EX characters are alot of fun, especially Mary. Tung Fu Rue is a real beast in this game, and Laurence Blood is really good too compared their RB2 versions. I just wish the game was faster and some commands in this game are pretty wonky. Kim is still retarded, although a less so than compared to RB1.
Real Bout 2 on the other hand I think is just the most solid of the bunch. Like I mentioned before, it's fast, it controls really nicely, and the commands for moves are streamlined and alot easier to do. I much prefer the RB2 versions of characters such as Andy, Joe, Franco, Mary Billy, Bob, Yamazaki and Hon-Fu. The Line Sway/Plane Shift system I enjoy more in this game since movement in and out of the background is faster, and it's a great Okizeme tool as well. I also prefer the combo system of this game, as there are way more chain combo's possible along with more cancelable moves, and feints are more useful too. I think giving P-Power moves a "super pause" was a step in the right direction too, since they all combo way easier now. I'll also say RB2 has my favorite version of Blue Mary, she just turns into a total monster when she uses her P-Power, Escalation. I'm fond of Geese in this game as well (Fuck Nightmare Geese!), although they took away Jaiken and Shippuken, he's now more reliant on his command throw(s) and his pursuit attack, along with being able to kara-cancel his back+B into anything. Which is yet another thing I like about this game, the number of kara cancels that exist, especially Mary's Kara M.Typhoon. I think this game would be really good if it just had real tick throws and maybe some kind of guard crush (both things Garou:MOTW implemented) since high level RB2 can get pretty defensive and it gets tough cracking open an opponent, especially if they are Kim or Billy and just Breakshot you all day. That's the last thing I wanted to mention, Breakshots were way harder to use in RB1 and RBS, but in RB2 they are way easier to use, and many characters have multiple breakshots, some of them supers even, and boy are they deadly... they are great if you are being presured and wanna break out some damage of your own, but being on the receiving end of one from a turtling opponent sucks lol.
Also, I see alot of people in this thread mentioning Garou:MOTW... which while I think is a great fighting game, I don't think it's a worthy successor to Fatal Fury at all in the gameplay department. Coming from RB2, it just feels really stripped down and I think Break Moves and Feints are a little too good in MOTW.
I'd say RB2 is actually the less tourney worthy of the two, because some stages have line switching and some don't. Combo execution is a little easier in RB2 (I think it might be because of the slight increase in speed) and, really, if you want to get down to numbers, RB2 actually has less characters.
In Versus Play, you will always fight in stages with line switching, unless you activate a dip switch to allow fighting in 1 line stages, so it's really not much of an issue.
Combo execution is easier in RB2 definitely though, mostly because of the very generous input buffer window, on top of commands being more streamlined.
Now I know Andy and Joe are way less potient in RB2 and Kim was nerfed silly. The thing I never saw with get togethers in RB2 is ridiculous overpowered character B.S. (Other then Tung Fu Rue but to me the character is just silly strong) like Kevin Rian is in MOTW.
I disagree, Andy and Joe are pretty solid in RB2, and Kim... nerfed? No way. Kim is ridiculous in RB2, easily Top 5.
And Tung Fu Rue is probably one of the weakest characters in RB2, he was way better in RBS for sure.
I'll say though... while Rick is like the most overpowered ridiculous character in RB2, I think he's one of the best boxers SNK ever designed next to Rob Python. Screw Vanessa though.