Most people I know and myself store food in bear bags. However, I have heard that some parks have banned bear bags and require canisters. I've also heard there is a bear in New York that has figured out how to open some bear canisters! Additionally, some of my friends have recommended bear canisters, but their reported advantage is usually limited to the bear canister makes a great stool!
In what situations does each method have an advantage?
"Better" might be the wrong question. Here are few alternatives:
"Safer" - Canister, hands down. Depending on where you are, bears have been known to study brilliant bear hangs, find the critical tie point 3 trees over, and with a casual flick of a claw, order takeout. On the other hand, I have seen bear canisters take a tumble off a several hundred foot cliff with no issues.
"Legally Required" - Often an area you are hiking will require the use of bear canisters (and if they do, will likely rent, or loan them out) due to the problems they have had.
"More Bear Friendly" - People think of bear-hangs / canisters as 'food protection' as in, "well, if I lose my food, I'll just hike out early..." Think of it instead from the bear's point of view. That free snack could send it down a life a crime, eventually resulting in its being relocated or exterminated. A fed bear is a dead bear.
So maybe "better" is the right word. Bear Canister - no question. Although it might add a little weight to your pack for a weekend, it might add years to a bear's life.
Better is often relative. I would not like having to carry a bear canister around as it is extra weight and bulk. However there are likely places where you will not have a tree suitable for hanging a bear bag, and the canister is the only way to go. It really depends on where you are going to be hiking.
One thing that hasn't been mentioned here is that in some places (especially in California - for example Yosemite and Sequoia National Parks) there are permanent bear boxes at popular overnight locations. It's entirely possible to do many interesting treks and rely entirely on these bear boxes. I've done this successfully in Sequoia and Kings Canyon.
On the East Coast at least, many bears are very savvy about finding ways to get your smelly yummy bear bag out of the trees. Even if a persistent bear fails to secure your food from the trees, his efforts to do so can cost you loss of sleep. I have personally had bears find shrewd ways of getting to my food bags twice on the Appalachian Trail. But that was a long time ago. For more than 25 years I have used a completely different technique. I put all food and smelly items inside a truly waterproof dry sack, and weigh it down with heavy rocks underwater in the nearest water source, secured by paracord to the nearest waterside tree. Apparently bears cannot learn about, much less get to, food bags that they cannot smell or see. The bag must be a truly waterproof dry sack, the kind used for kayaking. The paracord must be stout and securely tied, so you do not lose your food bag to a stream current. Dry sacs are heavier than regular nylon bear bags, but much lighter than a bear proof canister, which is truly a bear-proof plaything designed once again to deprive us of much-needed hiker sleep.
