Here are some differences
3.Nf3: Probably best if you intend 4.Nc3 (main lines), along with excluding e3, as 3...dxc4 is possible, but not so good. However, if you intend 4.e3 (to protect c4), black can develop with ...Bf5 or ...Bg4 because Nf3 puts less pressure on d5 so cxd5 and Qb3 ideas aren't effective (but 3.Nf3 and 4.e3 is still a good and trendy line).
3.Nc3: Good for playing 4.e3 (a useful idea for avoiding the classical slav, which is 4...dxc4 after Nf3 and Nc3), as 4...Bf5 there is answered strongly by 5.cxd5, cxd5 6.Qb3 with pressure (although besides the passive main line 6...Bc8 there, you may also have to look at the "Glasglow Kiss" 6...Nc6, a tricky gambit that requires good play from white to get an advantage). However, 3.Nc3 allows 3...dxc4 (as ...b5 can be followed with ...b4 to hit the white knight on c3, contrary to 3.Nf3), as well as 3...e5 (the Winawer Countergambit, which is tricky but still nice for white).
2.Nf3: if you're going to play queen's gambit lines, I don't see much point to this move order. With it, you avoid like the Albin Countergambit (sort of, 2...Nc6 and 3...e5 is still somewhat viable), but you also allow other reasonable options for black like 2...c5 or perhaps even a development of the queen's bishop on move 2 (as well as 2...Nf6, just heading for QG lines). Still, it's not a bad move order of course, especially if you play like the Torre or London against Indian lines.
So overall, it's an interesting debate. If you like to play Nf3 and Nc3 lines, play 3.Nf3 for sure, as you avoid the rather dangerous 3...dxc4 (Against 3.Nc3). However, if you despise the classical Slav (which why would you? White can choose lines to cater to his style of 6.Ne5 (more tactical) or 6.e3 (a little more positional)), try 3.Nc3 and 4.e3 (although it does limit you choice against the Semi Slav to the Meran or Anti-Meran). Of course, there are always specifics...
After 1.d4 d5 2. c4 c6 both 3.nc3 and 3.nf3 are both incredibly common.
I know that nf3 is aimed at preventing early e5 ideas. What are other differences in these lines? What is the draw back of nf3? In a vast majority of games I end up playing my N to f3 anyway and if I can avoid learning some albin gambit theory then it seems they way to go.
I have usually dogmatically played 3.nc3 not for any real reason; I just always have. Is there any theory I am avoiding by playing 3. nc3?
What about an even earlier 2. nf3 intending 3.c4 which seems to aim to prevent any chance at all for an early e5 from black except 1...e5. Are there draw backs to this move order. I suppose it black goes into the QGD instead of slav then you can't play any of the Ne2 ideas in the exchange variation.