Fretboard radius has a lot to do with how effective a capo is.
If they don’t match well, either the outside strings or the inside strings will not make great contact with the capo. Lots of companies solve this problem by using soft enough material to form properly to the fretboard despite the curvature mismatch.
I suspect, Rich, that your cheap capo matches that one guitar perfectly and the other not so well.
In my case (ha), I’ve got a 15 year old Elliott that matches my SCGC perfectly and is as sonically transparent a capo as I have ever heard.
I have a lovely Shubb I bought for my Telecaster, a model made for electrics, that has too much radius. So it doesn’t quite fit the Tele! Sounds rubbish. 🙂 I suspect the old elastic and rubber ones would sound great on the Tele.