cassettes CAN sound better than vinyl.

For you tape heads, any takers for my MC Hammer adams family cassingle?  Put your money where your mouth is.

Let’s think of the ways in which a CR-7 could be better than vinyl. Let’s assume that the Nak’s important caps have been bypassed by styrene or teflon, drive mechanism is belt rather than gear, and that the machine is otherwise to spec, and Dolby is not engaged; at least not Dolby C.

If one records a record onto a very good metal tape, say TDK MA (metal frame), or MA-XG (ceramic frame), then the difference between original and casette is small. Certainly less than the difference between a cold and a fully warmed up phono and cartridge.

So, if you carefully warm up your CR-7, your phono, and your cartridge, say 8 hours, 8 hours, 2 hours respectively, then your recordings should be better than a cold phono and cartridge. IMO.

So why don’t I do it? I like variety, and my cartridge may be immortal. And, oh yes, lazy, lazy ...

I used to record all my just-brought albums with a Nak and Maxell/TDK tape. Luckily I worked in an audio/record store at the time so could afford to do that. Although I could not say they sounded better then the LP, it was very close and great for everyday listening. It also kept the records pristine and was especially good when having several friends over having beers and such. Kept the records and even more important, the needle and turntable safe. Well worth it. I still have many of those tapes which are decades old now and they definitely sound better then MP3's even today.

@redwoodaudio 

"my MC Hammer adams family cassingle?  Put your money where your mouth is."

What on earth are you talking about? Is this some kind of famous thing like Fermat's Last Theorem? Or just ...?

The best cassette decks like the Nakamichi Dragon or any of several other high performance  Naks  (I have a 682ZX) or Tandberg or 3 head Tascams, using Dolby B, are capable of recording a signal with wider frequency bandwidth and less noise than mastering machines like the Scully and Ampex decks which were used for some of the most treasured recordings ever made. So does a cassette sound better than vinyl? It can, depending on the source of the music on the tape - and there will be no warp wow or inner groove distortion, and clicks, pops, and noise from groove wear will not spoil the sound of a tape like it will a vinyl LP with frequent playing.
A top quality cassette deck using metal or TDK or Maxell type II cassettes, properly aligned and biased, can give you a playbeck quality identical to what is being recorded, so whether it sounds better than vinyl is entirely dependent on how good the recording is - and yes, at its best it will absolutely destroy MP3’s, even 320K, and be as good or better than CDs.

Now, if what you’re talking about is a pre-recorded cassette compared to a record with the same music, being that the cassette was duplicated at a very high speed, typically 60 IPS, and from a second or third generation source tape - or worse, yes, the LP will sound better, at least when new.