under what circumstances would you use on or the other

Typically I would bed the action and free float the barrel...

For shooting paper, I would do both. For most hunting situations, neither one is necessary. The exception would be long range hunting.

For most local hunting this is probably true, but for a hunter that travels to a different areas I think that it makes good sense to bed and float. Humidity and temperature play hob with wooden stocks, and most plastic/fiberglass stocks are a bit flexible.

I always bed a 700 action when shooting magnum cartridges.

Most of mine are bedded and the barrel is floated. My Ultra Light Arms model 20 however is full length bedded and it shoots incredibly well for a 5lb rifle.

+ 1 for that...I couldn't get my 700 in 7mm Mag to shoot for beans till I beaded the action and relieved the barrel channel enough to get the barrel floated the whole length.

Most of my rifles are wood stocked, and bedding/floating seems to help...it certainly hasn't hurt any of them yet.

Free floating the barrel is only going to help you after the rifle heats up. I like going to the range and shooting paper so I like mine bedded and free floated on some of my rifles.

When you are big game hunting, it's not going to help at all, unless you plan on hitting the animal with your 6th shot(or so) after you heated up your barrel.

It certainly does help on most wooden stocks. The wood shrinks or swells a bit and can change the pressure on the barrel and on the action screws. My experience is that it takes several days for a wooden stock to settle if I am traveling from the Washington, DC area to the Colorado high country. Even after the stock has settled the usual pressure point between the stock and the barrel changes and can make that carefully crafted load into something else.

If you hunt without traveling far it probably does not make too much difference unless you manage to get the stock soaking wet.

On most synthetic stocks there is enough flex to change the forearm pressure a little (sometimes a bunch) when shooting with a sling or bipod. In general free floating is an inexpensive improvement for bolt action rifles.

Exactly!! I have several wood stock rifles that have been hunted with in the rain and snow for years, I have yet to have one move enough to change point of impact. If you are a target shooter and trying to milk every bit of accuracy out of your rifle then yeah, maybe. But then again if you are a target shooter and are serious about accuracy you just go buy you a H.S. Presision or a McMillian stock that has a full length aluminum bedding block.

These are not 'either/or' projects. You are not forced to choose one or the other.

Personally, I recommend doing both to almost all modern rifles. I have floated and bedded enough sporter rifles to believe in the benefits, even just for hunting rifles. Then again, I do shoot in pretty extremely varied environments, and expect longer range performance than some might.

If you are only going to do one, then it should be free floating. I don't know why you wouldn't go ahead and glass bed (other than trying to save money) when you do the float job, but it makes far less sense to me to glass bed the action then not free float the barrel.

Now, if you have some reason to believe you need to full length glass bed your action and barrel, rather than free floating the barrel, then go ahead. I don't believe in that.