I couldn't tell you all the specific reasons why, but I play so much better on sticks. Some of it is just because I grew up playing Street Fighter 2 in the arcades. Some of it is the button layout, like you say. But recently, Cesar from Area 5 came over and brought his SF4 stick (those giant $150 ones), and it seriously elevated my game in a very tangible way (over how I used to do with my Hori sticks). I decided I had to get one after that!

It's really just a preference. Hey, if people play much better on pad than on stick then by all means they should use it.

I kept having this discussion with some of my online friends. Personally, I don't see a boundary between good stick players and good pad players. It's easy to bandwagon onto the arcade stick faction because we see a lot of the big names rocking an arcade stick. What they don't realize is that these big name players like Valle, Wong, Daigo, and Ortiz have been playing Street Fighter since the arcade era. They're just accustomed to using arcade sticks.

Of course there are some benefits to using arcade sticks such as having multiple fingers assigned to various buttons, This in itself allows players to hold 3 punches for Boxer's turn-around punch and still attack, kara-grabing with Ken easier to execute, comboing out of Honda/Gen's slap chop easier,  and makes the advanced tactic known as plinking a breeze.

However, the recent wave of new players may have never played at an arcade at all. With that, a regular ps3 or 360 pad may be their primary weapon their most used to having. I've played with Vangief in various tournaments and every time I'm amazed how he can execute multiple link combos (with windows as small as 1 frame) consistantly in a match. Just by watching him, it's not the stick or pad that makes a skilled player. It's the practice and dedication that ultimately makes the most skilled player.

A good player will be good regardless of controller.

However, other than the walking 720, I don't see any other advantage the pad may have over a stick.

@Guillaume For most fighting games, I use sticks. For Melty Blood (my main game) i use controller since my character has a lot of overlapping moves (kinda like Seth). On stick, I'll occasionally get a hcf motion instead of an intended qcf motion. So controller can be more precise at times.

I really don't like the Dual Shock's D-Pad for fighters. There are some moves in Third Strike that I simply cannot perform on it. Honestly I think Nintendo is almost the only company that even makes good D-pads anymore. At the same time, everyone doesn't have $150 to spend on just a controller.

Fighting games aren't really designed to be used with a stick like one of the SRK users mentioned, because SF4 and many other fighting games are released on consoles, generally in far greater numbers compared to arcades. This is doubly important in North America, where arcades are much harder to find than in Japan. SF4, in particular, is pretty lenient on special move inputs, so that playing on a controller isn't as hard as it used to be in older games. The developers simply must design their game with controllers in mind, because that is what the vast majority of its players/consumers will be playing it with.

It really is a subjective matter, coming down to preference, price range, and prior experience, rather than either format being objectively superior.

Personally speaking, my preference varies from game to game, heavily dependent on the number of buttons the game uses and how they're associated with one another. Every time I pick up a console version of Street Fighter, I'm frustrated by Weak and Medium strikes being on the controller's face but Fierce strikes being on shoulders--it just feels wrong. On the other hand, a six-button game with four attack buttons plus, say, a "run" button and a "block" button works fine for me on a controller.

In the past, I actually preferred the PS2 controller for Tekken IV-V. I can't imagine I'd be able to put up with a PS3 or 360 controller, though--the analog triggers reduce the number of viable button inputs by 2, and for Tekken, I'm quite fond of using the spare buttons to map multi-button inputs that I have trouble hitting simultaneously. (I feel kinda like I'm cheating when I do that, but I fight better, so I get over it.)

I'd still love to get a fight stick, though. Not because I play a lot of fighting games, but because fight sticks recently have been getting really nice, and I'd really like to have something high-end and well-crafted for my gaming systems. (I'd probably use it mostly to play Pac-Man: Championship Edition, but still.)

Like was said previously, this debate is more a matter of personal preference.  Often many hardcore players will talk smack on pad players (due mostly to old school arcade vs console flame wars), but playing on pad is becoming more accepted.  You should always play on what you feel most comfortable and perform best on.  Each has its own advatages and disadvantages and most often these things will cater to what type of play style you have or that of the game your playing.  For example, like Daryl, I play Melty Blood specifically on pad due to the timing on inputs and the need to go to a nuetral position after each in order to avoid messing up commands.  You can go back to a nuetral position on a D-pad much easier and faster than on a stick.  However pretty much every other fighting game I play on stick.

IMO tho sticks do have a slight advantage.  When it comes to pads it is hard to get something that is custom to your tastes where on a stick you can customize all the parts to cater to your preferences.  American or Japanese stick?  Square or octo gate?  American or Japanese buttons?  Bat top or ball top?  With the newer Mad Catz and Hori sticks they make it easier to swap out and replace these parts.  With pads doing mods or replacing parts can be more of a hassle and often lead to you just needing to buy a completely new pad which really sucks if you spent the time to break it in or if its a pad no longer in production (like the PS1 Dual Shock Version 1 pad I prefer using).

@ Johnathan: I'm going to have to disagree with you on the matter of that newer fighting games are not designed for sticks.  Most of the fighting games coming out now on consoles all started out in the arcade or are based off a previous arcade control layout.  The move shortcuts in SF4 are there more make it easier for new players and the fact that many of the arcade sticks being released all use square gates by default which many players seem to have a problem doing 623 motions on.

For one reason or another, Street Fighter 4 really sunk its teeth into me, despite having never really gotten into anyh SF game prior. So much so that SSF4 was my most anticipated game of this year (and probably my favorite, in general, thus far, aside from Mario Galaxy 2) and I even dedicated myself to getting decent enough at it that I bought a fightstick at launch. I've been very pleased with my purchase - I was worried at first that I'd never be proficient with it, but the thing with fightsticks is that you have to train your muscle memory to work with it.

Once you can do that, it is physically easier (at least for me, but many others, too) to pull off the very specifically timing direction/button combinations needed for fighting moves, at least in an old-school fighter like Street Fighter.