Does the quality of your cards matter in terms of your score? For example, does First Premier/Credit One have any less weight that say American Express/Discover.
Do you stand a better chance of getting better credit cards and bigger CL's if you have AMEX/Discover/Chase on your report than say First Premier/Applied Bank?
There are 2 answers to your questions.
1) FICO doesn't care who the cards are from, be they AMEX or First Premier
2) FICO does look at util, AMEX or another prime card are likely to have a higher CL that will factor in.
Scoring-wise, the card "quality" does not have a direct impact. However, if your report is reviewed manually by a human being there is some clout that Amex/Chase/City/Discover have that could tell the underwriter that you're worth the risk of extending credit. There is also a stigma attached to Credit One/First Premier that also tells any intelligent human being that the person who has those cards (particularly in the absence of the more reputable credit cards) had credit issues in the past and may still be a risk.
As previous posters said accurately, fico doesn't care but manual underwriter might. However some internal scoring engines might care as well. The only real evidence I have seen is Amex rejections have cited not liking an open first premier card.