If you can get the gill methoud to work to remove the hook definitely the best option (and has worked for me countless times over the years). However, once in a blue moon they flat out just eat and swallow what you have or you can't get a good angle through the gills and so forth. In that case, cutting the line and leaving the hook is your best option. I've caught a number of fish that had a hook in them still that seemed fine, but everytime that happens I will still try the gill methoud on those when it's practical b/c it's obviously best to get it out if you can do so safely.
Anyway, I was never really sure if they could survive with the hook in there as there's so many theories on what might happen over time but a few weeks ago I caught a smallie that was about 3 lbs that actually had what looked like a 3/O hook that was frail and rusted sticking out of his bung hole He was in the process of passing the hook. I helped him out by pulling it out and there was a few inches of line still attached to it as well. Been bass fishing for about 15 years or so now and never seen that so was pretty psyched to finally get some confirmation that they can actually pass a hook like that.
Of course, the best thing overall is to minimize the chance of deep hooking in the first place by really paying close attention to what your doing and using proper tackle and technique. You can't avoid it entirely but you can most certainly reduce the frequency of how often it happens.
