I have a whole cast of old characters that I have tweaked for different settings. I usually do this when I see an RP that I think one of their personalities (or a few aspects of their personality - more on that later) would fit into well, and I take the core concept of the character and mold it in such a way that it fits the new setting. I still occasionally make new characters if I have a flash of inspiration for them, as well. It really depends on the setting and feel of an RP I'm joining. Whichever way I go, I always know immediately; somehow whenever I see a story that piques my interest I automatically know what sort of character I want to play, and that'll either be a stock character or a new build. I try not to deliberate on my characters too hard; usually whichever way my knee-jerk reaction goes, I follow it. 

Now, that being said, I do have one or two characters who I think are actually too well-established in their worlds to be adapted, mostly because it would feel wrong to put them anywhere else. Likewise I have characters who started as stock characters but developed into something different enough that I consider them separate from the character they're based on. (Funnily enough, I have one character who fits into both of these criteria). Usually I find myself adapting old characters more often than making new ones, but I think that's mostly coincidence, since I've done plenty of both recently. 

So yeah, for me it's kind of a knee-jerk thing, I do both. I really do like my legacy characters though, since I know them so well, and yet they still offer a new experience in every new setting I put them in. I also quite enjoy the process of adapting them, it's fun to see how set-in-stone traits can apply to new settings (ex. how can I take this character who's a priest in this world and play him in a world where religion is outlawed? How do I represent this set of twins as one character instead of two?).