I consider a "pass first" PG who'll look to get others involved first before they take their own shot. Nash of course comes to mind first. He can still score...can even be "the man"...but he works hard first to get the others involved.
A "shoot first" PG is like Baron Davis...is usually the high scorer and will take his shot if he considers it a "good shot" (this is sometimes and usually debatable)...but will rack up some assists because the D is queing on him.
Right now DJ "appears" to be the latter...but as I've said I think some of it is because he's very leary of pissing LB off (being a rook and all) and plays it too conservatively.
There's plenty of other threads on Felton, but since you asked I'd say his tendency is strongly to be a shoot first but is/can be a pretty good mix of the 2. That was LB's main task and the question of whether it could even be done (among other things like his contract) is probably what prompted the trade rumors. Supposedly LB is happy with Felton's progression...but it's definitely still a work in progress.
Personally, I don't want either but prefer a mix. Both types dominate the ball and I much prefer a passing/moving TEAM...which is what we're now building with Larry Brown Ball.
I think both PGs we have can be that...eventually.