What are the main differences between the versions?
Besides the library changes, Actionscript 3 is compiled for and run on a completely different virtual machine (AVM2), which was re-written from the ground up. It reportedly executes compiled AS3 code up to 10 times faster than code script compiled for the AVM1 virtual machine.
You should check out this doc for a list of differences between AS2 and AS3 as they can't be explained any better on SO :)