Nf3 or Bg5 in the Queen's Gambit?

After 1.d4 d5 2.c4 e6 3.Nc3 Nf6 is it better to play Nf3 or Bg5?

I play Bg5 which threatens winning the d5 pawn or messing up black's pawn structure unless if black plays a move like Be7 or c6. That's also what the video lessons and chess mentor recommends as the main line. However, Nf3 is a lot more popular than Bg5 according to the game explorer. What move is better and why?

There are often different transpositions with white wanting a QGD but wanting to avoid the Nimzo - possibly black's best reply to 1d4,c4,Nc3

Black can play :1 d4 Nf6 2c4 e6 threatening the Nimzo, then if white plays the safer or anemic Nf3, depending on your perspective, black can play d5 transposing back into a QGD avoiding the most forceful and statistically white favouring Botvinnik variation described in next paragraph.

If white plays his knight to c3 he can play Botvinnik's f3 idea later on within the exchange variation : 1d4 d5 2c4 e6 3Nc3 Nf6 4 cd ed 5Bg5 and eventually e4. Obviously with a knight on f3 white negates this possibility.

If white wants to play the best variation of the Queens Gambit Declined he has to either risk the Nimzo and have a line against it, or be prepared to get into via an English move order. Of course black doesn't have to offer the QGD in this instance and usually doesn't.

The popularity of the Catalan in modern times,may because of white's desire to avoid the Nimzo. Perhaps a better player than me can comment on this.

If the opening goes 1.d4 d5 2.c4 e6 3.Nc3 Nf6 and I'm white, I usually play cxd5, the Exchange variation. Otherwise, I'd prefer 4. Bg5 over 4. Nf3.

Usually I play 2. Nf3 if black plays 1...Nf6. I think the position with 4. Nf3 shows up a lot more often than with 4. Bg5 because black is playing ...d5 after 1...Nf6.

4. Bg5 does not actually threaten to win a pawn or mess up Black's pawn structure if Black plays a reasonable move. For example 1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. Bg5 Nbd7 5. cxd5 exd5 6. Nxd5?? Nxd5 7. Bxd8 Bd2+ 8. Qd2 Bxd2+ 9. Kxd2 Kxd8 and Black is up a piece. 4. Bg5 is the mainline. 4. Nf3's apperent populority is due to transpositions like the ones mentioned above. Chess tempo has 3...Nf6 being played 16,550 times and 4. Nf3 being played 30,993. 

Yes but sometimes I win a pawn in that opening. I am also thinking if black moves h6 after Nf3, it would be hard for white to develop the queenside bishop because after Bf4 black moves Nh5. However, I think the h-pawn is moved in the middlegame in more than 50% of games with kingside castling so I don't think moving h6 on the 4th move is bad.

Neither, play 4. cxd5 ;]

Actually, Bg5 is the main line, but Nf3 is also fine, it doesn't make big difference.