cassettes CAN sound better than vinyl.

cassettes CAN sound better than vinyl. with a good type ii and a Nakamichi CR-7
I would never say cassette is better than vinyl. However, I was in a studio in Rochester NY in the 80s and they were using NAD monitor series decks to record my friend's band. The resulting demo tape was outstanding. I also got to listen to demos from other bands and they too were amazing. I heard a demo from a local jazz band, Cabo Frio, which blew me away. I went out the next day and bought the NAD. I still have it, no longer use it for much other than old Dead bootlegs and a few other boots I cannot find in digital format. I never heard an MP3 that sounds as good as a tape made from the NAD or a couple NAK Dragons my friends still own. 

I had a Nak head unit in my 87 Mustang GT. The system in that car was better than many had in their homes. The installer told me the Nak would not skip on bumps at high speeds. Trying to prove him wrong I popped in some Little Feat and I took him for a test drive at 100mph over some RR tracks. He wasn't lying. Never skipped a beat. 
There's really no comparison. For example, that's why tape deck manufacturers used -20dB levels when they quoted frequency response for cassette decks. You really don't want to know what it looks like at 0 dB.
Music doesn't have high frequencies at 0dB.  One of the problems was self biasing of the tape by high frequencies in the music.  Higher bias lowers distortions but limits the bandwidth at high frequencies (tradeoff) .  My Aiwa deck had HX-Pro that is basically a servo on the bias (keeps total bias constant).  It greatly extended frequency response of the tapes.  Still, it was not even close to modest TT I had, even with best tapes.  CAN it sound better than vinyl?  Of course.  8-track can sound better than vinyl if you get really cheap crappy TT.

If anyone on this planet thinks an optimum sound system designed around an optimum cassette deck, Nakamichi or no, can sound better than an optimum or even a modest high-end system designed around a vinyl source (i.e. decent TT) playing at concert or performance level gain, then please tell me what you’re smokin’ because I want some of that! Now, admittedly, I’ve never heard or spent quality time with a Nakamichi deck but 1 & 7/8 IPS? Really? Even when recorded from a live source, under optimum conditions, on a quality multi-head cassette machine, in Dolby B/C HX-Pro on the best metal tape, there’s no way! Of course, this is IMHO. Now, 15 IPS on a quality reel to reel machine? Well, that’s a whole other story! Again, IMHO, 3.75 IPS is better and 7.5 IPS better still but no way better than vinyl!

It was cool to read about your MCS deck. I had several of them in the late 70s and early 80s; forget which models. They got me started in this hobby (really an old table-top tube AM radio did) and I've just gone further and further down the rabbit hole. Back in the day, with a decent deck and table, the deck was pretty close. I had the Teac R999-X and it was very very good though as at least one other posted mentioned, those machines of the time had mechanical trouble fairly regularly. I lived near the Teac facility and could take it there, but it always cost me over a hundred bucks to get it back. For me, I always bought the record, recorded for the car, and put the vinyl away. Was fun thinking about this, thanks OP for starting this thread.
I can see a reel to reel master tape sounding better then vinyl .
Nakamichi Dragon was the best of the best , and if cassette 
Was of good quality it can sound very respectable .
not as good as a top  turntable which is $$.