For rifle, that would be .308. Great cartridge, and the firearms are not as heavy, as larger calibers.
For pistol, I am going to have to say .45ACP, bigger holes is always better. It's a tougher choice as I like 9mm, 40S&W and 10mm a lot too. Depends on why and where I am carrying.
I would have to say I have no favorites I LOVE THEM ALL. But I really like shooting my 17hmr first and then my .223 for rifles (not to leave out my 30/30 and for pistol .45 then 9mm next. Heck they are all FUN to shoot! Having said all of that, this statement only reflects the choice of ammo from a selection of what I own, not what I would desire.
It would depend on what I'm doing. My favorite general purpose cartridge is probably the 7.62x39mm. I can use that for defensive purposes and it also is good for hunting in heavy brush, as its ballistics are very similar to .30-30. My favorite handgun round is definitely the .40 S&W with .357 Magnum being a close second. They're the only two calibers that I have a handgun chambered in. If we're talking a traditional "hunting" rifle round, it would be the .30-30 for the same reasons as the 7.62x39mm. I love a good .30-30 lever gun. I also like the .357 for use in a lever gun. If going with a bolt gun, it's .308 or .30-06. I like both of those rounds equally.