My database has 1603 games in the line
1.d4 d5 2.Nf3 Bg4, with Black scoring a poor 41.3%. (Contrast this with White scoring 54% over 38,587 games in the Trompowsky.) In particular, White does very well with the two responses that Steinitz used in the Chigorin match:
3.Ne5 leaves Black with a dismal 33.9% score, while
3.c4 leaves Black with a 34.7% score. So the numbers tell the story that this line is considerably worse for Black than the Trompowsky is for White, which explains why it isn't played much. (Nigel Short appears to be the only top player in recent times to play the line even a handful of times; he did score a nice rapid game win against Kasparov with it in 1987 though.)
Why the disparity in results, though? Well, the only difference between what White is getting in the Trompowsky and what Black is getting in your line is that White has gotten in the extra move
d4; but that's a pretty significant extra tempo. To illustrate with just one concrete line, after e.g.
3.Ne5 BF5 in your line, White can strike Black's center immediately with
4.c4 and have a good game. In the Trompowsky, on the other hand, Black couldn't really do the same with
2...Ne4 3.Bf4 c5?!, since White could kick the knight and then push ahead in the center with something like
1.d4 Nf6 2.Bg5 Ne4 3.Bf4 c5?! 4.f3 Nf6 5.d5 d6 6.e4
when White has grabbed a lot of space and Black will lag behind in development. This is just an illustration, but the point is that White having already gotten in
d4 is a significant plus.
So this line of Chigorin's really isn't good, but if you're interested in playing something like it, a better version can be had via
1.d4 d6 2.Nf3 Bg4, the Wade Defense (which I play myself sometimes). Now
3.Ne5 is no longer an option, and we have something much more playable for Black. Julian Hodgson himself (who greatly popularized the Trompowsky for White) has played this particular line quite a bit, which is good evidence that this is a fine way to play. (Not to mention, it's been played on occasion by folks like Petrosian, Anand, Grischuk, Ivanchuk, Svidler ...) Of course, playing
1.d4 d6 means having to be ready for the transposition into
e4 lines via
2.e4, but if you're OK with that, then this is a perfectly good choice for Black.