Lee Valley also has this trim puller, which might have a little more finesse, Trim puller
I'd vote for the Lee Valley item, that looks quite useful. The 2 best features is that it's thin and it's wide.
I've pulled a lot of trim and most of the pullers out there are relatively narrow and have a thick, sharp bevel to the blade. Unfortunately that combination leaves small indents in the top edge of the trim strips. I've resorted to scoring the trim first and then sliding in a couple of wide drywall knives behind the trim and try to leverage the trim from the wall a little bit at a time.
As others have said, don't try to force the nails back through the surface of the trim, pull them through the back or cut them off.
When cutting the nails, I prefer a RA grinder with a .040" thick abrasive disc because you can trim the nail flush with the wood surface. Using nippers will always leave a little nub left hanging out the back.