Well, the dive shop I certified with would not allow us to bring our own gear. The rule was we had to have our own mask, snorkel, boots and fins. They provided everything else. This particular shop had mid level Scuba Pro regs and BCD's. I did purchase my own wet suit because the ones they had were tight in the chest and it felt like my breathing was being restricted.
I asked why they wanted everyone to use their stuff and they said, "we want all the students to use the same equipment so they were all familiar with it and that would keep things easy." They also said that it might be nice to train on the "usual" type gear so if we were ever in a location with no gear and had to rent we would be familiar with what the local dive shop on site was likely to rent....makes good sense to me and have no regrets with the way I was trained.
I quickly bought my own gear and in fact I pretty much had everything before we did our check out dives{still couldn't use it though}. I bought good stuff, at least I think it is, if money is an indicator then what I bought should be beyond fantastic. The one purchase I am second guessing is a so called "safe second" or Air II type reg in lieu of the standard octo...Seemed like a good idea at the time I first came to know of it's existence. Having one less hose had to be a good thing, but now I am not so sure...for the life of me I cannot find any real advantage to it.