It depends what the purpose of the dive is. If you are going down with the aim of taking good photos, then chasing something will not lead to a good photograph (Personally I'm not a huge fan of far of fishes rear ends anyway!) and you would be much better saying that at least you saw it and move on to something else.
However, if it is the diving mindset that you have on, then chasing after somethings can be more beneficial. For instance, sting rays that were on the bottom will only move a short distance away etc.. however chasing after things is much more likely to spook it again as you go charging in, and then you probably won't see it again.
Like David said, chances are that if you are having to chase after it then it is unlikely that you could catch up to get a good look. On the other hand, if you have gone all the way to some exotic destination to see a certain fish, and you will never see it again (possibly ever) then chasing it can be your only option - at least you have tried to get a closer look; if it swims off again then you'll know that it just wasn't meant to be.. It can be better than living with the regret: "if only I'd followed it...."
Then depending on how interesting the subject is (some fish species indigenous to one location really aren't that interesting
) chances are I would chase it for a little bit, but only if i thought there was a good chance I could keep up. But then it is the diving that is my priority rather than the photography. The only time I would never chase something in these circumstances are when it would either be dangerous too (i.e. a current would pull you away from the reef wall or something/get lost etc.) or when it would spoil it for other people - say some other photographers were waiting down the reef a little for the subject to swim in front of them, and chasing it would scare it so that they wouldn't get chance to look.