I like it both ways depending on the situation. I set my alarm 20-30 minutes before I need to actually get up so I can go back to sleep for a bit. If those 20-30 minutes feel like 2 hours, that's awsome.
However, I also love the nights when you sleep completely sound the whole night. When I wake up, I feel like it's 4 in the morning and I'll have to go to sleep again. Realizing it's actually time to get up and you just slept solid the whole night is refreshing.