AMC also broadcasts in HD (where available), which probably boosts their popularity/ratings a great deal.
Personally, I don't see how anyone can stand to watch a film on AMC - HD or not. They edit out any and all "objectionable" content, show tons of commercials, and force pretty much everything into 16:9 on their HD channel, regardless of the original aspect ratio. It's almost the worst possible way to watch a film.
Of course, I know I'm preaching to the choir here.. my point is, you can't really compare TCM & AMC. It's like comparing a fine wine with something that comes in a box - two completely different target markets.