It's really a bad idea to paint yourself in one or the other. I know it's tempting because it would be simpler and also because "client speak" often comes from a "camped" direction. But remember clients usually DONT KNOW much about this stuff... or worse they know buzz words.
Really Bruce Lee had the best philosophy , apply what is useful.
I like to base myself on the following points, which you may already know:
1) There is/was better support for floats than AP/RP for quite a while. This is not so much of a issue today, but as you should strive for your pages to support as many browsers and versions it is something I consider. Seriously if it wasn't for browser support... display:inline-block/-moz-inline box does wonders.
2) AP really takes element out of the flow.. so its difficult to build in such a way were layout elements interact with each other.
3) More importantly, AP causes a mentality designer/client thing in size and position instead of flow and flexibility. It really lends to the WYSIWYG mentally which should be avoided like the plague.
4) HOWEVER for some things, depending on the specific application, AP/RP is a life and bandwidth saver. (again taking into consideration browser support)