One of the big differences between the Cessnas and the Pipers is the nosegear. I think on most nosewheel pipers the nosewheel is hard connected to the pedals. So, if you do a crosswind landing, and touch the nose down with the rudder in, the airplane will dart to the side because of the offset nosewheel. In a Cessna nosedragger, the oleo strut lets the wheel spin where it may until it is compressed. So, when you plonk the nose down with a bunch of rudder, the wheel lines up with the direction of travel, and nothing unusual happens. But it's been years since I've flown a nosewheel cessna or piper, and I'm not sure how broadly this applies.
I also found, while at a low experience level, that it was easier to do a decent landing in the Pipers near max GW. I think the ground effect helps out a bit.
When I was a student pilot, I flew to Oshkosh with a guy that owned a Cherokee 6. He didn't understand the whole crosswind thing. Touched down crooked every time, my little tailwheel brain kept about shorting out. Last one was a biiig crosswind, he first had a big crab, but was looking out my window at the runway. So he straightened out the 6 without dipping the wing & using opposite rudder, so we immediately blew off centerline. He got us back on centerline in the big crab, then repeated the whole cycle. All 3 miles of final we did this dance. Finally touched down with that big crab angle, and I can vouch that the main gear on a Cherokee 6 is stout! Never was I so amazed to not have perished. It was an excellent way to learn crosswind, you can learn from a bad example surely as a good one.
-- IFMU