What makes tape sound better than vinyl ?

Maxell Metal Vertex is the very best cassette tape, and my deck is not even specifically calibrated for it.
I'll get Otari or Studer open reel deck in time and then the turntable, any turntable, will not sound better in any aspect. I will also be able to play master tape dubs if I can find them. 
Yes, I too think the resonances in vinyl playback is a big factor, but I suspect it's not the whole story.

Its impossible to get audiophile sound from a car system

True, but you can Audiomobile sound..close enough. 

All important recordings are originally on tapes, R2R. Is it just me who still after all these decades keeps wondering why this best media never came popular. Vinyl records, c cassette tapes, CDs and all that modern digital finally put the R2R into museum, so to speak... Shame, isn´t it ?

BIG SHAME !!!
But it's not in museum, there is a number of people very serious about R2R recording and playback.
Vinyl is great for archive, though, and back-up.

stringreen
Its impossible to get audiophile sound from a car system.

>>>Let’s get real. It’s impossible to get audiophile sound from many HOME SYSTEMS. More to the point, it’s possible to get very good sound from car systems. WITHOUT much effort. Let’s see, you got battery power, no house AC issues, the car is metal so act as as RFI/EMI shield. Obviously you'd want to replace the fuse with an aftermarket fuse and the acoustic space in a car is small, a lot like near field listening, no worries about having to use a lot of acoustic treatment. Maybe a little wouldn’t hurt. One assumes the CD player buffers the data so you don’t have to worry about vibration, anyway the shock absorbers act as a seismic vibration system for very low frequencies. Finally use audio cassettes anyway. They sound better. Problem solved!