Burn vs Steinitz in the french defence.

I've started learning openings more in depth now, and i'm not sure wether to play 4. e5 or 4.Bg5 when facing the classical french. I'm looking for the most aggressive and tactical out of the two options.

Just to be clear the classical french is 1. e4, e6 2. d4, d5 3. Nc3, Nf6

Thanks,

The Burn is 4 Bg5 dxe4, but there is also the MacCutcheon 4 Bg5 Bb4 and the Classical 4 Bg5 Be7, which splits into 5 e5 Nbd7 and now either the Classical 6 Bxe7 or the Alekhine-Chatard 6 h4.

4 e5 is most in fashion now.
Fischer used to play 4 Bg5 so as to trade his bad bishop Bc1 on the color of his own pawns away preferably for black's good bishop Bf8 not on the color of his pawns.

All of those lines lead to a kingside attack for White given the direction the pawns point, but if you are looking for that immediate attack and expect to win in 25 moves like in the Smith-Moron Gambit, you are dreaming.

The Steinitz I can tell you is the harder one to face, though I only play 3...Nf6 maybe one in every 10 or so cases of 1.e4 e6 2.d4 d5 3.Nc3. Most of the time, I play 3...Bb4.

My recommendation would be to play 4. Bg5... there are some very aggressive lines like the alekhine-chatard attack, though it depends on what your opponent plays. It's also worth noting that lines in 4. Bg5 can be transposed into from the BlackBurn french, Trompowsky, and Veresov. The tranasposition from the Blackburn is nice since you'll need a line against that regardless. 
This setup won't always lead to a burn, though... 
4. Bg5 Be7 5. e5 Nd7 6. h4 Bxg5 - this is the alekhine chatard attack, white scores extremely well here and the lines are complex / aggressive / interesting. 
4. Bg5 Bb4 5. e5 h6 6. Bd2 - I find this position is also quite interesting and nice for white, similar to a winawer but feels more stable for white
 
The only real issue I have with 4. Bg5 is in burn itself. It's a good position for white, and white scores well, but it usually involves an early trade and experience shows it's hard to get much happening in the kingside attack. However, you are still often castling queenside and launching your pawns toward the king regardless, and you will pretty much always be the one on the attack. It's hard to go wrong... you just usually have to play the attack for endgame advantages. Still if you know the lines well there are interesting variations that can get aggressive.