I recently applied for an AMEX Blue Sky and Discover Miles card and I was denied from AMEX (after about 2 weeks) because "I wasn't an amex cardmember for long" (I got the AMEX green charge card a couple months prior), and because "I had too many hard pulls on my credit report". When I checked I only had 2 pulls, one was from AMEX themselves for the green charge card...
Discover on the other hand took their sweet time (2 weeks) to contact me, and as I posted earlier in another board on this forum, they didn't approve me instantly because my household income (the income I gave them on the report) was different from my personal income...How they had that information I dont know, I never banked with Discover and this was my first card with them. Nonetheless they approved me for a generous credit limit 8,300 - at least in my opinion.
FYI my credit score is ~735 and I have low balances on all my cards (some with no carried balance), no BK, 0 negative hits on my report, always on time payments, decent income and age on accounts.
In short, from my experience, AMEX Credit Cards are harder to get than Discover, or any other CC for that matter, but hey, they obviously don't want my business so its their loss.
If you are in college, the student version will be much easier to get.