I don't see how ground mobility is effected by either choice.
These have alternate mobility constraints and benefits. Saying one is strictly better than the other doesn't paint an objective picture.
Double Sticking - When performing the aerial, your left-right mobility is hindered (as you must be pressing up to input the control stick jump) but you can perform reverse aerials with ease. You can also perform frame perfect up air inputs by setting the c-stick to "attack."
Button Jumping - When performing the aerial, your left-right mobility is hindered in a different way, since you must be holding the direction of the aerial you want to input. So if you want to do a retreating fair, for instance, you must hold forward long enough for the desired aerial to be executed, then hold backwards. This messes with spacing and such. However, it has the benefit of retaining advancing aerials and RAR type movements, since you are pressing the direction you desire already and holding it after the aerial comes out. This method lacks a way to input frame perfect up airs.