Yeah I play DOA with three buttons too and it happens also to me lol. When people see me playing with three buttons they are like "what!?" But it's funny, cos it's how the game should be played. Anyway yeah, it depends on the preference of the player. I personally prefer the arcade stick (especially when I play 2D fighting games), so I only play on it, even if I'm able to do everything also on a pad.
On the arcade stick pressing different combinations of buttons (right hand) is easy and you can also increase the chances of success on doing some just frames (e.g. you hit the button once with your middlefinger, release it to neutral and hit the button immediatly again with your forefinger, giving you two potential imputs - if you play SF you will also find P-Linking easier with the stick). But on your left hand you have a large range of motion (e.g. from neutral to forward there is quite a distance to achieve), while with the d-pad you can be faster cos it's very small so it requires a shorter movement to hit a direction. So for example if you are going to try to react to some moves (like seeable lows, etc.) with the d-pad you have an advantage. These are some of the differences between arcade stick and pad in my opinion.
