What makes tape sound better than vinyl ?

If you are saying that transferring cd's or vinyl to tapes sounds better then you are saying that the transfer is not an accurate transfer and that the distortion that the tape is adding is one that pleases you. There is nothing wrong with that but you do have to admit that you just introduced a uphonic distortion. 

Now if you are saying that a live mic feed is more accurately captured on tape, rather than vinyl or digital then you are saying that tape is a more honest format for capturing truth. IMO, tape using Dolby S is right up there with the best.

However, most here are reporting on the former not the later. I doubt that tape is correcting for the flaws in vinyl or digital and, in that case, it is the processing distortion you are enjoying. Not that there is anything wrong with that.

While recording from anything to tape some coloration is inevitably added but it's not the whole story and it's not necessarilly what is found pleasing. Tape recorder 'rearranges' the elements of the incoming signal and lays them down to tape. This rearranged source might in some respects give better soundscape. Something like that, in its own way, might also happen when you record digital from digital. In other words, processing may yield better results.
Do you know what some crazy Japanese do? They have 100 volts wall current over there. They take it up to 230 volts with one step up transformer and then take it back down to 100 volts with another and claim that it sounds better. This is just an analogy and an example of a rather primitive current processing. Things are not that simple.

I'll stick with what I stated. Your's is more than a bit murky.  But, hey, it's your pleasure not mine and in the end that's what matters. Enjoy!

send paper can make vinyl sound worse than tape.

Digitally remastered Audio Cassettes Sound much more analog than their CD counterparts. Smooth and dynamic. More dynamic than CD, in fact. Example: Kind of Blue, digitally remastered on cassette kills.