I like both as well.
RPGs I prefer to be offline. I just want a good plot and atmosphere, and that's not the case with MMORPGs (well WoW has atmosphere actually..)
Some shooters are good offline as well, HLČ for example.
But other than that: online all the way!
I play Warcraft TFT online
Unreal Tournament 2004
Sometimes Jk: JA
My favourite online game is Warcraft though. Been playing it for 4 years online now. The community is big, there are countless custom made maps (one of them even made it into E-sports), and the normal game itself requires so much skill.. you can always improve yourself and will not get bored.
Online gaming with a nice clan and friends just beats all.