I find the difference between warm and neutral papers to be quite subtle. The difference is in the overall image tone. I also understand that the "warmth" can be increased by using specific warm tone developers. It is said that warm tone paper reacts more noticeably to selenium and other toners. I have used both Ilford fiber paper in neutral and warm versions and they are top quality papers. I recently tried a Foma fiber paper called "Chamois" which had a nice matt surface, and a very warm yellow/brown base colour. It gives a very different look to any other paper I have tried.
Alex