I'm not sure I understand your question. Are you asking whether canceling the Cap1 card will help you get approved by Amex?
It sounds like you had an old chargeoff or something with Amex. If you have issues with getting approved, I would imagine that is the issue as opposed to the Cap1 card. I wouldn't do anything until you have a decision and a reason for the decision. If the denial says something about you seeking new credit, you could ask whether canceling that card would matter on a recon.
Starting Score: ~500 (12/01/2008)
maybe... but I have a really hard time putting them in the same category lol. Zync is geared for a younger crowd and the minimum qualifications are a little more relaxed, at least in terms of the length of positive history required... but it has a decent rewards program, access to the usual amex benefits, a low AF (until you start adding packs). It's petty much like any other amex charge card in terms of not having a pre-defined limit... there are people with tons of history with amex who have extremely high internal limits that switched over to zync. It doesn't let you accumulate MR points or allow airport lounge access, but neither do many of the other cards. I thought it was a good fit for my needs though.
AMEX just has their own system of deciding. They may approve someone with a 650 FICO and deny someone with one in the mid 700's depending on the circumstance. Cap 1 gives high interest, AF starter cards to almost anyone. They have no rewards on those cards (unless it's the sub-prime no-hassle)... honestly having had an amex card in the past I think there's a world of difference between the two companies and their minimum offerings. But that's just my honest opinion. 
@Anonymous wrote:maybe... but I have a really hard time putting them in the same category lol. Zync is geared for a younger crowd and the minimum qualifications are a little more relaxed, at least in terms of the length of positive history required... but it has a decent rewards program, access to the usual amex benefits, a low AF (until you start adding packs). It's petty much like any other amex charge card in terms of not having a pre-defined limit... there are people with tons of history with amex who have extremely high internal limits that switched over to zync. It doesn't let you accumulate MR points or allow airport lounge access, but neither do many of the other cards. I thought it was a good fit for my needs though.
AMEX just has their own system of deciding. They may approve someone with a 650 FICO and deny someone with one in the mid 700's depending on the circumstance. Cap 1 gives high interest, AF starter cards to almost anyone. They have no rewards on those cards (unless it's the sub-prime no-hassle)... honestly having had an amex card in the past I think there's a world of difference between the two companies and their minimum offerings. But that's just my honest opinion.
If you're interested in accumulating MR points, just doint cash in any of your MR Express points you earn with the Zync. You can add an MR eligible card at any time down the road and all of your MR Express points, that you accumulated while paying the lower AF of the Zync, will be upgraded to regular MR points.
So after all this craziness Amex approved me... Fully expecting an F/R now 
...but then since I pay immediately maybe I'll luck out. More seriously though... thinking of using their premium car rental insurance on my trip in two weeks.