Supine triceps extensions seem to be more effective for me, and they are more enjoyable to boot.
I think the supported position allows me to focus more on the move, and to really put a 'squeeze' on the triceps muscles without feeling I'm possibly overstretching the shoulder area.
There is more room for the arms to move in different planes (ie: cross-body triceps extensions) and with different angles (start with hands in neutral at bottom, then turn to prone at top of move) without worrying about my head getting in the way!
I can also more easily self spot or do forced negative reps in this position.
It's a great position for super-setting: do lying dumbell tri extensions until you can't continue with good form, then finish off with tricep bench presses.
I also have to say that I have a particular fondness for this exercise vs. overhead extensions, as, back in the day when I was working out in the college weight room, the supine barbell triceps extension was the first exercise that brought any definition to that area for me (I'd previously been doing tricep pressdowns and overhead extensions, but didn't see the results until I added the lying extensions).