Walnut always looks a bit dead, White Hart a bit posh, Not seen enough of Rose and Crown to form an opinion... but I haven't been in any of them so happy to be guided.
Walnut Tree has indeed been pretty quiet whenever we have visited (apart from 'that night').
White Hart is the same ownership as the Angel and Harp, I believe, so fairly food-biased?
Rose and Crown looks to have gone upmarket since we were last in there, judging by the lack of pork puppets on their menu. (Also indicated by the very existence of a menu!)