I used a courier/messenger bag for the first three months of my commuting. It had a waist-to-shoulder main strap and an adjustable waist strap to keep the bag in place. It was quick to pack, quick to remove and could hold quite a lot. However when packing it quite full, say with groceries, it was noticibly uncomfortable, even with no box edges poking me, and I would always choose the quickest way home rather than enjoy my ride.
I switched to panniers, after weeks of thinking about it, and tentatively buying an Arkel Urban Utility Basket after seeing them recommended by someone else on this board (had to order from the US too - I'm in UK!). My first few rides without a messenger bag, which I had gotten used to, I felt as free as a bird! Now with two Arkel panniers, I find I can buy almost double the amount of groceries and still cycle around in comfort, not really noticing the added weight, at least not on flat ground.
Unless actually planning a shopping trip, I only ever take one pannier. I have been known to fill one pannier however with food, and it does not unbalance my bike at all, at least not noticibly, unless I am not on it i.e. it is unbalanced only if I am walking the bike.