I vote limiting mobility because the more mobility you have the more freedom you have to play your game.
Limiting attack options is one of those "on paper" arguments but don't necessarily hold true in practice. For example you will often hear players say "this is a good matchup because I can blow up all of their wake up attacks so all I need is one knockdown." or "My pokes beat all of their pokes", "my anti-air beats all their air attacks free and leads to 50% damage + corner carry". What these players often don't take into consideration is that their opponent doesn't have to wake up attack, press buttons or jump.
Your 60% anti-air is only relevant if your opponent jumps in on you. If they stay grounded the whole game you lost an illusory advantage. Same with wake up attacks. You might be able to stuff all of their options but if they just happen to have solid defense and make all the right blocks and throw techs then you don't really have any real advantage. And it's the same with pokes.
One of the best examples of this "economy of options" is Snake Eyez beating Ricky Ortiz's anti-Gief Rufus:
Justin Wong and Ricky Ortiz have developed a Rufus tactic that on the surface appears to shut down Gief's main gameplan completely: They just stay outside of SPD range and harass him with cr.fierce, sweep and occasional s.mk. If Gief tries to go for his best footsie buttons, he gets blown up or pushed back, if he tries to jump he eats EX Snake Strike.
So what does Snake Eyez do? He chooses the option of doing nothing. If he doesn't jump, you can't anti-air him and if he doesn't press buttons you can't counter hit him. Knowing Ricky is just trying to stay out of SPD range, he decides to walk and block, walk and block. Until Ricky corners himself. Since all the normals he's blocking don't inflict chip, all Snake Eyez needs is a few hits/trades and/or one or two SPD to win.
That's a great example of breaking down an already broken down matchup, adjusting to your opponent by not giving them what they want and beating them at their own game. It goes to show that matchup numbers are only a starting point.