It's really like comparing WalMart and Target. Home Depot has low price points on all types of items, and is very competitive. If you are shopping for the basics - lumber, nails, concrete, etc. Home Depot will have great prices. If you want a washing machine that washes, folds and puts away the clothes, then Lowes is the place. They will carry a lot of higher end items.
Lowes. I don't like Home Depot because they generally build right across the street from an old, established Lowe's. They are so similar, I don't know if it matters where you shop. Personally, I can find what I need at Ace Hardware.
Very similar, but slight leanings in this way: Home Depot if you're looking for materials to build or repair something. Lowe's if you're looking for small appliances, window treatments or other things to add to the comfort of your home.