Any sheep is going to struggle with constant wetness, both with feet and fluke.
However, as said, some breeds are better than others.
But a point that many on here seem to miss totally, is that there is probably more variation within breeds than between them.
I.E A hardy welsh breed, from a small flock that is pampered, not culled for problems, and comes from very different ground (no matter where they were meant to come from traditionally) is going to struggle on a very different system . . . . . . . . . whereas even a traditionally 'softer' breed, if selected and culled hard, and from similar ground, is going to do better.
The most important thing is to go see the sheep, and check they are currently doing what you want them to do at yours.
I run wool shedders of a couple of types, and cull them hard for any issues, and they generally live, lamb and grow well on marginal ground here, cause me little bother, and do well enough commercially.