As a hardcore SSF4AE player I'll tell you flat out, execution in SF is on an 8-way axis instead of a 4 (so what is Down Forward to us is Down Down-Forward Forward to SF) SF also supports shortcuts (which will drive you insane at times) but makes some things easier on you.
To be blunt, SF is a much more technical game and at the lower echelons of play outdoes lower tier Mortal Kombat play easily, it has a lot more systems and its very footsie based. It will teach you some good habits if you learn to play it, and it's a good jumping point to a large variety of other fighting games.
Personally I just picked up Blazblue CS2 with my cousin recently for the sake of expanding our skillset, Blazblue is a very very fast paced fighter with so many mechanics (Air dashing and Air blocking, Breakers, Parrying (like block parrying), Push Blocking, Fatalities, Hypers, each character even has a unique mechanic) it's taught me a lot and its inputs are very specific and because of that (similar to 3rd Strike) its made me a lot better at fighting games in general when it comes to executing and timing what I want when I want. It is a very skill-intensive game and I'd recommend picking it up if you want to learn some advanced fighting game techniques that branch into other fighting games well.
But SF is a great game, don't let Capcom haters drive you off or complain about it, to each their own on the fun factor but it was my first fighting game (save for Soul Calibur) and it really brought me into the genre as a whole. Enjoyable characters, great gameplay, and competitive factor even at lower ends makes for enjoyable gameplay.
Oh and coming from Mortal Kombat, block stun is nill in this game, so do NOT throw crap out just to put pressure most of the time, you'll do a lot more baiting than you do in MK (where you can randomly throw out some strings without fear of retribution at times just because of the insane block stun comparatively)
To break down big name fighting games that will teach you skills (if you seek to improve your skillset)
Street Fighter 3rd Strike (Parrying, Exact Execution, tight combos, Hypers) - Very specific combo windows and execution required for your moves, a parrying system that with proper timing and practice you can fully negate even the most ridiculous moves if you're skilled enough. Very skilled, very intricate, highly technical footsies game. 8-way Axis.
Street Fighter 4 (Focus attacks, Loose Execution, tight combos, Hypers) - With things like focus dash cancelling and tight combo windows, SF4 can teach you a lot of good techniques and reactions, as well as improving your footies game across the board. It teaches you how to pressure without putting yourself in compromising positions and teach you a skillset that easily transfers to other fighting games. 8-way Axis.
Marvel vs Capcom (Air blocking, push blocking, super jumping, hypers, loose and tight combos) - Its a very juggling game, you're playing with three characters and studying their assists, and how they interact with eachother to perform the largest combos. It has a lot of baiting, a lot of footsies, and a ton of positioning. 8-way Axis.
BlazBlue (Everything) - Blazblue's combo system is a little loose at times, but has some tight ones as well, this game will teach you the epitome of timing and reaction when appropriate. Characters have a large variety of tools, every one of them is unique to an extreme degree (some feel like they're from other fighting games entirely). It has so many systems pulled from other games that it will VASTLY improve your technical aspects when you return to playing other games. It taught me how to properly dash with a fight stick. Also its absolute insanity when both players know what they're doing and it'll greatly improve your reaction time. 8-Way Axis
Mortal Kombat (Breakers, EX attacks, hypers, fatalities) - Mortal Kombat has heavy hitstun and a good mix of loose combos and tight ones, a lot of its earlier combos (dial-a-kombo into special) are really easily, put off some nice damage, however some of its later combos require extreme execution and buffering/cancelling to properly perform. The breaker system is very nice (but never carry the habit of it into other fighting games, as, save for Blazblue, they really don't have such a thing) and gameplay is super fast paced mental chess at the higher levels. Will teach you how to tighten your combos and effectively dish them out more properly since the entire game revolves around them to an extreme degree. Also, mind games. 4-Way Axis
Thats the last one I ever played until this new one. And to be honest I like UMK3 better. This nw one is awesome but I like oldschool stuff, lest techincal I guess, Im kinda braindead so it suits me lol 
. Because I want to know anyways.
