I'm assuming that by favorite, the question is asking for "All around", and not just for a specific job.
Given that, I've gotta vote for the .22, with the 9mm running a very...very.... close second.
The reason being, there's very little a handgun caliber can do that I've not done with a .22.... Plinking, target shooting, hunting... and yes, even self-defense.
It's cheap to shoot, accurate, easy to find, easy to handle, and guns for it aren't exactly scarce, in varying sizes, shapes and manners of function. Plus, if you know what you're doing, it'll put anything you're likely to encounter flat on it's back in short order.
If I were forced to say which center fire round was my favorite, then it would be the 9mm Para, since it's about as useful/flexible/"Utilitarian". But for all around, from just plain fun to "dead serious", the .22 Lr. gets the nod.
No matter what, I could live quite happily with nothing more than guns chambered for one of those two rounds, if that were required. ( Glad it's not, but still... )
J.C.