Personally, I like to do the straight back version at the end of my squat days and the curl up version as a finisher on deadlift / back days.
Straight Back Extension (aka Back Raise):
- no real extension of the back , spine stays in the same place -> works isometric only
Curl Up Back Extension:
- hips locked
- flexing, extending the spine
Greg Everett says about back extensions that they
- can be done every day before and/or after training
- hold weight behind your neck instead of in front of your chest
- alternate between days on which you use resistance and days on which you do the reps unweighted
When / How do you do them?