I've never heard Yes-shows, but I have Yes-songs double disc set. Which of the two are better?
Define "better."
Yessongs (no dash) was originally released as a triple LP, whereas Yesshows (also no dash) was a double LP, so the former has more material. The former also has the entirety of Close to the Edge (both the song and the album, as well as some of the band's most iconic songs like Yours Is No Disgrace, Heart of the Sunrise and Roundabout. You also get Steve Howe's Mood for a Day, an extended version of The Fish and excerpts from Rick Wakeman's Six Wive's of Henry VIII (no solo spot from White). Yessongs was entirely recorded during the Close to the Edge tour (and mostly during a six week period in November and December 1972).
You get no repeats on Yesshows (other than the recorded Firebird Suite intro),* and most of the songs are from TFTO, Relayer, GFTO and Tomato. You get The Gates of Delirium in its entirety and an extended (if you can believe that) version of Ritual. There only a couple negatives about Yesshows (IMO). The first is that, on the original LP version, Ritual was split between sides 3 and 4. That was an unavoidable necessity given that the total run time is nearly 32 minutes. On the CD version, Ritual is all on one CD, but it's still split between two tracks with the fade out and and fade in that you got on the LP version. I have to assume (but don't really know) that this couldn't have been fixed when the album was mastered for CD. The second negative is that it doesn't include a live version of Awaken. On the other hand, notwithstanding the split track, the live performance of Ritual is OUTSTANDING, and the live version of Gates might be better than the studio version. Note also that the performance of Ritual came from the Relayer tour and, therefore, featured Patrick Moraz, rather than Rick Wakeman. Yesshows features recordings from the Relayer, GFTO and Tormato tours.
* - Looking at Wikipedia, I'm seeing that there's a CD version of Yesshows that has performances of I've Seen All Good People and Roundabout, both of which are also on Yessongs. Although these are different live versions than you get on Yessongs, they are the same live versions from the CD release of Classic Yes.
I don't have any issues with production qualify of either album (although I can't disagree with what Orbert wrote), so the question "better" probably comes down to what songs you like better or simply the run time of the albums.
Then buy them both anyway, because they're both great.
Yup.