As a permanent green card holder you have all the rights (- one) and responsibilities as a citizen. As a green card holder you can not vote. That's about it.
If you want to differentiate:
A US born citizens has all rights and responsibilities.
A naturalized citizen has the above but the citizenship can be revoked
A green card holder (permanent) has the above minus the right to vote.
Oh yeah, and a green card holder can not be part of the TSA Pre-Approved program yet a green card holder can be a part of the trusted traveler program.