What makes tape sound better than vinyl ?

Tape was an imperfect medium that degraded the sound. You may like that particular flavour, but it cannot possibly be an improvement if accuracy is the criterion. As a demonstration that it is indeed an alteration (and hence degradation), tape sound can be emulated very accurately in plug ins. See here, for example: https://www.waves.com/plugins/j37-tape#butch-vig-billy-bush-j37
Another way to investigate this is to do muliple passes of the copying: make a copy of a copy of a copy. After a number of generations there is nothing left worth listening to.

A flawed original can be copied to be made better in the same way photoshop can enhance a picture, but it is no longer an original. If that is your end game, you are better off getting an equalizer. 

I find cassettes generally sound very musical, rich and natural. By comparison CD generally sound thin and bland and "uninteresting." Oddly, perhaps, I find cassettes that are digitally remastered sound quite good - very analog and detailed with better dynamic range than their CD counterparts in many cases. Case in point - Kind of Blue digitally remastered on cassette is very dynamic, detailed and lush. It appears cassettes went out of style and production just about the time overly aggressive dynamic range compression reared it’s ugly head for CDs, later on for vinyl.

Those who like cassettes may like compression - a more punchy sound. Cassette will definitely compress good vinyl. Good vinyl can have as much as 70dB dynamic range on the outer edge. Cassettes never exceeded 50 dB.

There is no need to feel ashamed that you prefer lower quality compressed audio - a lot depends on the quality of your playback system - compression in a modest car audio system usually works great and this alone probably lead to the success of cassettes (walkman and making your own compilation tapes are other factors). Of course from a sound quality perspective cassettes were a big step backwards.

Just speculating here I’d say the main factors for Tape possibly sounding arguably ‘better’ revolve around:
Bandwidth. Dynamic Range. Resolution.

Then or as well, the Mastering and duplicating Process… the playback device itself, the tape material, the bias applied to the particular tape material, and the original Master’s integrity prior to the conversion.

It could be here as simple as the devices have disparity in playback . resolution, TT vs Tape.

If everything here is home made, DIY duplications the factors are greater the duplicated version loses resolution during the process of CD > Tape, or TT > Tape. Merely the input/output connections demand a Db or so of loss for each set.

Regardless thereason, or IMHO, the reasons, it seems Inna has stumbled onto a scenario that has improved his ability to enjoy music.

I’ve found merely ripping CDs to lossey codecs then burning them back to CD and thereafter ripping to lossless codecs (which was not done intentionally) served to remove the roughness, aggressiveness, upper end brittleness the orig CD possessed in varying degrees.

Is it then more enjoyable? My jury is still out. Although, I’ve kept those files. Listen to them as frequently as nay others, so for me, its all good.

My enjoyment level does not hinge on the numbers associated with a digital track, only its sound.

Now and then, merely ‘different’ is indeed better.