having a 4-way in the middle of your panel, with appropriate buttonage will give you a better playing experience than switching one of your 8-ways to a 4-way. Pretty much because it's in the center, and not off to one side.
Also, some games definitely benefit from a 4-way joystick... Donkey king for example... with an 8-way, Mario tends to "freeze" when getting off of ladders because you're hitting a diagionals instead of straights. Pac-man can get confused as well, and don't get me started with q*bert.

Yes. go with a dedicated 4-way stick, and put it in the middle of the panel.

Or make a swappable control panel, and swap out the controller configurations for what games you want to play!

Good Luck!