Constant aeration is a really good way to go for yeast starters. But since you usually only can add oxygen to wort at the beginning of fermentation, I think that oxygenation is a better way to go over aeration to begin your fermentation. You do have to be careful and not overdo it with oxygen since you can bring the dissolved oxygen levels much higher than you can with aeration. Excessive oxygen levels MAY create higher alcohols and more solventy perceptions in the finished beer. I have not seen definitive proof of that, but several prominent brewers have mentioned they notice it.
I use an in-line sintered stainless stone followed by 25 ft of transfer tubing after my chiller. That gives me the chance to introduce a fine stream of oxygen bubbles into the wort and it has a good chance to transfer to the wort before dumping into my fermenter.
You don't want to drop a hose into your wort and blast it with oxygen for a minute. You want to use a stone and introduce very fine bubbles at a very low rate for a much longer time. I probably have my oxygen tank on for 10 minutes during the transfer, but its at a very low rate. I probably get 10 to 12 (5 gal) batches from one of those little red disposable oxygen cylinders, so I don't think I'm overdosing the wort. My ferments are rapid and strong (a good starter helps too). If you're dropping a oxygenation stone into the bottom of your fermenter, you should reduce the oxygenation rate until you can just barely see fine bubbles coming to the surface and let that go for many minutes. How many is many? I can't say for sure, but I've mentioned my duration above.