I very much prefer the AVR over PIC, whose architecture I find a bit messy. This may be just me, and it won't trouble you if you can write in a high level language, most likely (some dialect of) C.
Since you're new to microcontrollers I presume performance will not be the issue, so instead I would look for availability of development tools: prototyping boards, IDE and simulation/debugging tools. Personally I liked AVR Studio (Atmel's free development environment) a lot.
Jason mentions the TI's MSP430, which is an excellent controller indeed, especially if you're in very low power applications. But I wouldn't recommend it for a newbie, since configuration is a bit cumbersome. (I recall that the description of the oscillator covered 20+ pages in the user manual.)
