cassettes CAN sound better than vinyl.

Better?

I'm not sure about better...

Especially if you incorporate the impact of time on tape recordings....

You can get the top end of a cassette to sound pretty good but there is not enough tape width to get all the low frequency stuff. And then we got to ask about your source. Prerecorded cassettes? They are awful. Digital? OK with me. From an LP? Can't do better than the original.  

You can get the top end of a cassette to sound pretty good but there is not enough tape width to get all the low frequency stuff.

@russ69  Actually its the tape speed that says what the bass will do, coupled with how much gain the tape head preamp will have. At some point the designer cuts off the bandwidth because with each octave lower another 6dB of gain is required (one of the side effects being that hum can become a problem). The faster the tape speed, the harder it is to play bass for this reason. 1/78 ips isn't all that fast.

I thought tape width, depth, and speed were all involved.