I also play higher stakes live than online - live, I play $1/$2 up to $6/$12, but online I play $.05/$.10.
I'm transitioning to online from being a live player - I'm finding online players to generally be better than live players. They're also tighter/shorter stacked - implied
odds are bigger in the games I play live than online. The live games I play have tourists and casino regulars coming through regularly (who buy in for as much as 300 BB's) - the fish are huge in these games (and have large bankrolls), so I haven't had to work much on my strategy to make money in live games, my mistakes are generally a lot smaller than the other players'.
Not the case for me online - my mistakes are not offset as much by the mistakes from other online players. I've had to make a lot of changes in the way I play to suit online play - more positional awareness primarily. These changes have been benefitting my live play as well, though...