What makes tape sound better than vinyl ?

I don't find that to be true for cassettes vs vinyl.

I use well-tuned Nakamichi 682ZX with custom transformer with Maxell Vertex tapes. Recordings from cds also sound better than cds, in the same aspects. Cassette is just a mini reel, four track, slow speed. But of course I meant mostly open reel decks. Still, it's the tape.

No.
There is no way to improve a given signal.
It can be possible that the tape has higher gain in the output stage and this can give the impession of better dynamics / detail in a given stereo system.