alright so ive always played fighting games like sfa3,sf3rd strike and the other sf3’s ,sf2 alright fk it ive played every sf game but i actually started playing sf4 seriously instead of random button mashing and spamming of moves on the other sf’s but what ive noticed is that it takes really good execution in the other sf’s to pull off moves i switch to a fightstick and im noticing that im actually improving with more of my links,specials,supers etc thanks to playing the old sf games so if anyone actually wants to get there execution better they should play the other sf’s because they dont rely on that input shorcut like sf4 so when u do play sf3 and decide to play some sf4 matches in the future u will actually notice a difference. so basically you will rely on the skill u have of knowing that you dont need a shortcut to pull of moves. All this stuff does relate to pad too because its practically the same thing as a fightsticks when it comes to inputs.
I think with pads, it’s hard to get exact inputs down, so they put the shortcuts in. So I guess if you train your self to get really precise with a pad in older games, it would carry into the newer ones too. Though it’s honestly just better to stick with a stick.
for pads though i think it goes by wat kind of pad it is too like if practiced alot on diffrent pads like the sega pads,xbox pads and playstation pads up until the madcatz pads they put out its sort of the same thing related to fightsticks because you are taking one type of feeling that you had from one pad and evolving it to the next pad until you getting the input of the move down by heart because you know the feeling of the moves inputs but i will agree with you that pads might be harder just for the simple fact of changes of pads its not like a fight stick where you have 3 diffrent changes you can go by like the changes of gates if you own a stick you could always modify how you would want your fight stick to feel you cant really mod a pad unless you want to light up the buttons with some leds lol.
forget 3rd strike, if you wanna better your execution boot up ST 
i’m a newbie and focus mainly on ST and it is a dick when it comes to inputs, they have to be done +perfectly and fast, i also have a fightstick and after a few months i still havn’t gotten the DP down, i main Guile as charge characters are almost made for square gates
It’s super hard to plink on a pad, so at least in sf4 I’d say sticks are a lot easier to use.
Except that for SF4 Pad users can double tap for the same effect.
I believe it all comes down to preference and comfort.