Not all diapers are made the same. What works for one baby doesn't necessarily work well for another baby. Pampers (Swaddlers and Cruisers NOT BabyDry) are what seem to works best for my children. I get my diapers through Amazon.com, and it is one of the cheapest options that I have found yet. You can often 'clip' a coupon on their website to save money. Sign up to be an amazon mom (free) to get a certain percentage off of diapers. Do subscribe and save to save another percentage. I currently save 20% on every order, AND it ships to my house for free.
Do some price comparisons on the different websites and see how much it is costing you per diaper. Then you will know whether or not the gift cards would be better spent on diapers or something else. I will say that my experience with Babies R Us is that their diapers are much more pricey.