What makes tape sound better than vinyl ?

Yes she is, appreciate the sentiments good people, long may she continue to "rock it out". 

The example I was thinking of is the way I put my reel to use; record vinyl to reel for convenience, this is constant with few variables, no matter how good the vinyl rig is, the reel playback will sound better.

I use 2 track recorded at 7 1/2 ips. The vinyl is recorded tape out on pre, to tape in on reel. As I explained, the reason the vinyl sounds better on playback, is because the sound is bigger because of the larger tape heads of a 2 track, not only does that mean more detail, but it also adds depth to the sound stage.

I know that's not the same situation as you might expect from the original statement, but I record my vinyl to reel for convenience, and that's what I get. When you compare different turntable setups to different reels, that's not valid because no constants have been stated.

Recording directly from phono stage to tape is better than using preamp out. Unless, of course, you can't do it because you use onboard phono stage. That's an additional advantage of having separate phono.
I rarely listen to entire album and often have to move the needle, I make compilations on tape, though in my case of a cassette deck turntable sounds better overall. If I had good two track open reel deck I would only touch turntable when recording to tape. Each record would be basically played once - to record. They would remain in top condition for the archive and cartridge would last for at least ten years. Yeah, it's Studer, mono blocks and speakers. Preamp is not needed.

In regards to a cassette deck, what would be your recommendations based on current good used equipment still in circulation?
Might be a fun worthwhile endeavour especially as I still have a huge pile of tapes from when I used to play them in my muscle cars before switching over to Hidden Stereo systems which were then cd/ fm based not cassette/fm based as the old indash spindle fit systems were.
Not sure on budget as have not considered tape in a long while but my guess is that $300 to $350 should get something halfway decent?

Thank you
Kevin

Kevin, I took a look at what's available on ebay right now. I can see that prices for good decks are going up. Of what I saw the closest to your price range that I would bother with is Nakamichi 582 for around $600 including shipping. The seller promises to service the deck before shipping it. Those old decks really need service form time to time. I have no personal experience with Nak 582 but it's good. I read a lot about cassette decks years ago before choosing Nak 682ZX, which is I believe the best performance value. Couple of extra hundreds of dollars go a long way when it comes to cassette decks. But if you are very serious there is a rare Nak ZX-9 for $1400 serviced by Willy Hermann. That's where I service my deck. He currently does only overhauls which is in fact not full overhaul but partial overhaul, including all the calibrations, alignment, transport disassembly etc. For my deck he charges about $650, I do it every five or six years.