Some comparisons:

Hardfork is making some invalid transactions valid

Softfork is making some valid transactions invalid

Hardfork requires the consensus of vast majority of miners, users, and merchants

Softfork requires the consensus of vast majority of miners, but not necessarily non-mining users and merchants

Hardfork can change any rules in the protocol or implement any new rules

Softfork is usually less powerful (with a trick which I call "Aux block", a softfork could also be very powerful: https://bitcointalk.org/index.php?topic=283746.0)