Even the dry way can get wet. My 2nd or 3rd ever caving trip, some time in the late 70s, I was one of ~10 kids going down (on ladders) with a few adults. There were some other people going down the wet way (on rope, I think).
While we were down there must have been a serious downpour, and the pitches were very wet on ascent - the ladders seemed to be surrounded by solid water, but it was probably ony really heavy spray. However, there was enough to make ascent scary and breathing tricky at times, and it would have been difficult or impossible for lightweight kids without serious pull-assistance from above.
It had rained so heavily that water was running down the Pennine Way track and pouring into the dry entrance. Some hurried damming stopped that and diverted the water down the wet way (by that time, the party on the wet route were already out and helping with the damming), but I vaguely remember someone later saying that some water had been [re-]emerging from a hole in the wall somewhere near the last pitch, though I've looked since and can't quite think where.
Of course, with SRT, such flooding in the 'dry' route would likely not be so much of a problem for people getting out, though the entrance pitch could be a bit sporting, and I think it's a pretty rare occurence.
I do remember the wet way as being slippy even in dry-ish weather. With the pitch only being a short way in, is it possible to leave a line from surface in case of higher water?