I fight Fightstick players all the time using a standard Xbox One Controller. Having a different controller doesn’t put you at a disadvantage. To be truthfully honest, here’s an example: I play Super Smash Bros. for 3DS & Wii U both:
With a 3DS.
I can still do great and take down tons of people using Controllers like the GameCube Controller. it’s just practicing with what you prefer, but I don’t think it should be so drastic as to separate them into matchmaking. Plus, more people have a controller than a fightstick anyways, due to the Fightstick being higher in price, and (Its a bit intimidating for some people IMO).