see attached link, we tried priorsdale a long time ago and it looked blocked... a long drive out for not much gain.. and i seem to remember having to drive through a ford to get there so don't go when the rivers are swollen!
http://ukcaving.com/board/index.php?topic=1195.0
also did tutman's hole near alston; that was quite good although i seem to remember it was a bit of a walk from the car.
lastly, i remember trying to find ayleburn mine caves once and wasted a few hours looking for the entrance in an area that looked like the forestry commission had recently re engineered the whole river bank.. the entrance was no where to be seen!
so in a nutshell, not better than the dales but something different to try!
lastly, i'm guessing you've tried Nenthead mines? they are well worth a visit, the club used to go quite a lot....absolutely masses to see in there...
graham