Van geet or Reti ?

There's a long history of dogma against the Van Geet... but nowdays the dogma is breaking down. The critical line - the only objectively testing line - which the engine scores about equal... is where black plays 1... d5. This punishes the fact that the Van Geet 1. Nc3 doesn't adhere to classical chess principles. Specifically the knight blocks in the c pawn and the d5 pawn restricts its movement, white will need to build up to e4 at some point and try to liberate this knight. In the meantime white can't take up as much space in the center as he usually can with a d4/c4 setup. What white does get, though, is more initiative with the forward knight / the ability to castle queenside and push the kingside pawns. So it's more of an attacking move, which isn't as traditional. In contrast the Reti doesn't really violate any significant chess principles.

Most notably 1. Nc3 d5, the critical Van Geet line, can be transposed into the Jobava London... the Jobava only became popular and respected starting in 2016 when Jobava / Rapport won a number of high level critical games with it. Other GMs then started exploring it at that time. In contrast, the history of chess theory stretches back to around the 16th century... that's when the italian was first played. For all of that time no one considered the Jobava to be a serious opening and it wasn't played, and the Van Geet was also considered dubious. So there's just this very long history of chess that the Van Geet is missing from. You won't find the Van Geet mentioned in most chess books, or the Jobava for that matter.

The Jobava usually leads to a big kingside pawn expansion / queenside castle and very attacking chess.

Nowdays it's much harder to make the case against the Van Geet, because you have now many GMs who play the Jobava and advocate for it. In general chess has been moving away from the highly theoretical lines and players have been focusing less on objective engine eval, players don't mind equality as much as they used to. The strength of engines has led to a much greater emphasis on playing attacking chess, and moves which may be uncommon but get your opponent out of book. This throwing off of the opponent is something the Van Geet does very well, largely because it's missing from the history books, and there are actually many unique Van Geet lines against many of blacks responses... in the future it may not throw people off as well. At that point I can see it being used as a complimentary system to 1. e4. But for now it throws people off extremely well. For all these reasons the Van Geet is looking like a better option and is being advocated for by certain GMs such as Simon Williams, Nakamura, and others... So I think chess theory is kind of catching up with the Van Geet and it's starting to get some acknowledgement.

Van Geet and Reti are both very transpositional. In general... Van Geet transposes well with 1. e4 lines. The chigorin / "jobava" setup is unique amongst 1. d4 openings in that most sidelines leading up to it end up being 1. e4 sidelines - i.e. you can run into the caro-kann, french, pirc, etc. The whole chigorin system also combines very well with a 1. e4 repertoire. Though powerful in its own right, I sort of see the Van Geet as the complimentary system to 1. e4.

In contrast... the Reti transposes very well with 1. d4 lines. There are some exceptions, like some places it can transpose with the sicilian, but in general it's mainly 1. d4.

So as far as the important theoretical distinction I think that's the clearest way of thinking about it - Van Geet is a complimentary transpositional e4 system, the Reti is a d4 system... Van Geet is more attacking but violates some classical chess principles in doing so, the Reti is more classical and positional. And the Van Geet actually has more unique lines than the Reti / is still rare, whereas the Reti is pretty common.