I haven't seen either show, but I'm very acquainted with the popular opinions on both shows, so this should and hopefully is somewhat helpful.
Venus In Fur has been praised for the performances, especially Nina Arianda who is giving one of the most riveting performance on Broadway this season. Reception to the show itself - meaning strength of the book, etc. - is mostly positive with a few dissenters that found it a little boring or trite. Everyone says that the performances in the show elevate the material.
That isn't the case with The Lyons, however, as even Linda Lavin, who is also giving a great performance, can't salvage a amateurish second act. Most say the first act is the best of the three, with the third being pretty decent, but a horribly sloppy and unenjoyable second act that ruins the show for most people.
If I had to chose between the two, I'd probably go with Venus in Fur, sheerly because it is a tremendously unique show, while The Lyons is a fairly traditional, i.e. stale, dysfunctional family drama. The performances in both are the selling points, as Arianda and Lavin are giving terrific performances.
I actually just got back from seeing "The Lyons." In short, Linda Lavin is excellent, the first act is funny and focused, the second act is aimless, tonally weird, and, surprisingly, doesn't even focus on Linda Lavin's character much. I honestly don't know where the playwright was going with that.
I haven't seen "Venus in Fur," so I can't comment.
Do whatever you can to see BOTH. Trying to decide between the two is like asking Sophie to once again play favorites with her kids. The two shows dish up an electric night of theatre. Two different animals arguing appearance versus reality through two seperate lens. In the end what really makes them must see for any theatre lover bolis down to two words - Arianda/Lavin.
Thanks for the input, guys! I ended up booking a ticket for Venus In Fur.
The deciding factor for me was the fact that the show is closing on June 17th. All the other shows that were on my "must see" list -- The Lyons, Peter And The Starcatcher, and One Man, Two Guvnors -- haven't set a closing date yet. I haven't read anything either about the original cast members (Linda Lavin, Adam Chanler-Berat, Christian Borle, James Corden, etc) leaving soon. I'm keeping my fingers crossed that I make it back to New York before that happens. Unfortunately, I only have one day to spend in NYC during this trip and I could only squeeze in two shows. :(
Thanks again! I'm excited to see Once and Venus In Fur!