It really varies from residency to residency. Choosing one depends on what you want to get out of it. Some will give you tons of experience in bread and butter dentistry - operative, fixed, removable, endo. Others have a more surgical focus. Some do lots of IV sedation; others do none.
There are many different reasons for doing a GPR. Are you looking to improve your CV to apply for specialty programs? Do you feel unprepared to enter private practice? Are you hoping to gain specific new skills before entering the real world?
Some GPRs are competitive, but there are always seats that go unfilled every year. If just anything will do, you will definitely match somewhere. Pay varies from a small stipend ~$10,000 to as high as ~$45,000. Usually hospital-associated residencies pay the best because they get GME funding.
As far as hospital duties go, the residents at my school take a lot of emergency call for dental issues at the ER. (Remember, you will no longer be a student in your GPR; you will be Dr. Tim.) They also rotate for brief periods through different areas of the hospital though I am vague on the specifics.
I hope some others chime in.