PhotoDiode vs LDR for fast laser pointer detection?

A photodiode will be plenty fast. I would guess almost any photodiode will give you millisecond timing resolution as you request. In fact, almost any photodiode should be able to do a factor of one thousand better than that (microsecond resolution). You would need a fast photodiode to get nanosecond resolution, but you don' need that. The more important issue will be electronics for detecting the photodiode and firing the flash. I'm not sure if you are asking about the photodiode itself, or if you are looking for a packaged photodiode. But either way, a millisecond is quite slow on electronics time scales. I would be surprised if you could find a photodiode that is too slow for you.