What makes tape sound better than vinyl ?

This is an interesting conversation. The best playback in magnetic tape would be a half track machine running at 15ips and recorded directly from the studio master which most likely would have been 2".
Tape (of any sort) also has potential problems such as drop outs (metal particles actually falling off the tape) and having levels set too high during the recording process leading to "print through". I would love to be able to hear music played back from a first generation half track format. Unfortunately, tape degrades over time and is not a stable source. That's why we have digital now.

I have couple of Vertex cassettes that I played more than 500 times. I almost never rewind or fastforward. They still play just as good as when they were new. And this particular tape is Maxell back coated tape that they used it their reels. They might be good for 500 more plays, I'll see. 
You can also modify decks, add outboard tube playback head amp, have custom headblocks for two track and four track recordings and playback and do other things. Great open reel deck is a true audiophile machine. You can even use it as an active preamp, as I sometimes do.

It might be one of the big ironies of audio that tapes degrade, even though I suspect when properly cared for it’s probably not a huge problem, and that’s why digital came along. Another big irony is that solid state replaced tube electronics due to "reliability issues." Cassettes when cared for just a little do not degrade. First, tape has been the first step in most recordings ever since digital first reared its ugly head. Second because digital has been playing second fiddle to vinyl and even cassettes like forever in some VERY important respects such as emotional involvement and musicality. Yes, I know what you’re thinking, "But digital is getting better!" Perfect Sound Forever! Horray! 😛

Doug Sax proved the superiority of direct-to-disk LP's over tape recording way back in the early 70's. Take a direct mic feed from a band playing live, record it onto the best tape machine you have (even the best in the world, that of Water Lily's Kavi Alexander), and cut a d-2-d LP at the same time, comparing the two formats to the direct feed. The d-2-d wins, hands down. Compare a d-2-d LP to any tape recording you can name. No contest.  

Yeah, some guys 'bake' the tape, use LAST tape and head preservatives and do other things. I use LAST head preservative that ideally should be applied before playing each cassette. My deck probably has 5000-6000 hours of playtime on it and the head has a minimal wear.