It is the switches in those that are clicking. The X-Arcade switches are notoriously "clicky". You can change just the switches to Cherry microswitches, and that will reduce the clickiness quite a bit...but it will still be there.
Street Fighters and other fighters pretty much all use microswitch based joysticks, but if you really want to get rid of the clicks, you will have to go with some leaf joysticks.
But, I think you will be happier by just replacing the switches, IMHO.
If you do go with Happ's, then the Competition Joysticks seem to be what is favoured for fighters.
Hope this helps!