FYI -- The Costco brand diapers are the same as Huggies Ultratrim diapers. Kimberly Clark makes them both -- same diaper, different brand names. The Sam's brand diapers are different from all the others, and tended to run small.
I'm not sure if Costco does this, but the Pampers diapers at Sam's had a size 1-2, which is an "in-between" size. It wasn't very useful to us because they're too small for a baby who wears size 2 diapers, but rather big on a baby who wears size 1.
We've only ever had a Sam's card.
We have always gotten better diaper deals with coupons. Babies R Us will have great deals like $5 of any box of Pampers or Huggies, plus they will take manufacturers coupons on top of that. Since there are plenty of $2 coupons, we got great deals there. Get on the diaper and formula manufacturer websites and sign up for their mailing lists. You'll get all kinds of samples and coupons in the mail.
Also, the smaller "jumbo" pack diapers often go on sale for $6.99 or $7.99 at grocery stores, Target, etc.. When you couple that with a $2 coupon, it's a great deal too. It takes 4 or 5 of those little packages to get through a month, whereas one of the big boxes is about a month (in the beginning that is -- you go through fewer diapers as they get older).
Either way though, we kept the diaper budget around $30/month.
Sam's did have great deals on formula. Especially if you use the Parent's Choice brand (the Walmart store brand). They've expanded the types of formula for that brand -- now they offer soy, lactose-free, and even organic. It's always significantly less expensive than the national brands. I believe that it was $5 to $10 less per 32 oz can than Enfamil (for the powdered formula).
For the national brands I didn't notice any difference between Sam's and Babies R Us. We used Carnation Good Start with our first (after nursing for 6 months), and Parent's Choice soy-based formula with our second (after nursing for 4 months).
Congratulations!