AMOLED has superior contrast (can do true black). It doesn't ghost nearly as much with fast moving objects. The viewing angle is also much better. The "lighting" is even.
Downside is it doesn't last as long as LCD, tend to burn-in with static images on screen like CRTs and Plasma TVs would. They cost more right now.
LCDs have relatively poor contrast (can't do true black), poor viewing angle, and slow response time making them tend to ghost much more. They tend to have areas of the screen that are brighter/more washed out than others (due to backlighting). They do last longer though. LCDs are dirt cheap.