I play about the same, though I do try to walk longer distances from time to time.
I used to say I played better walking, but that may have just been more of "what I was used to" even though I may have previously attributed it to "feeling the course beneath my feet" or some other such thing.
Also, poll added. Let's try to do these types of things, people.
I have no idea, as I've never tracked this sort of thing. I think I've had good and bad rounds both walking and riding. I prefer to walk when it's allowed, but only because I like to walk. There's really no quality of play variable involved in that decision.
BTW - I lived near Amsterdam for a couple years back in the 90's. Kan je nederlands praten?
I used to believe that I played much better walking but one thing I've noticed since I've moved is that the difference seems less. The real issue, IMO, has to do with pace of play. Before I moved walking fit perfectly into the pace of the courses - relatively little standing around. If I rode there was a lot of hurry up and wait. Here I find the pace of play a little faster for various reasons so when I ride there's less standing around.
FWIW - I do find walking easier on my back and joints than riding in a cart. I know it makes so sense since you are exerting a lot more energy walking, but the jolting of the cart and the getting in and out of the cart is much harder on my body - that can lead to better playing.