Consumers cannot pull their own Experian FICO scores, so unless you got that Experian score from a lender, then it is what we call a "FAKO" score. Consumers can only pull their own Equifax and TransUnion FICO scores.
There is an abundance of companies out there selling credit scores, but any and all scores aside from FICO scores do not matter. Banks don't use them, and they can/do have totally different scoring algorithms. Lenders only care about FICO scores, and therefore you should only care about your FICO score.
From which bureau is the FICO score you're referencing?
As to reasons why your FICO score might be different across the different bureaus: you might have inquiries/derogatory items on one report and not another, lenders might be reporting your cards differently across each report, each FICO scoring algorithm might weigh certain type of accounts differently (charge/open accounts on TU 98, for example), etc etc.
What I would suggest doing is pulling all 3 of your credit reports from www.annualcreditreport.com. This is the official site to obtain all of your REPORTS (not scores), and you can do it once a year for free. You can cross reference the data on these reports and determine why one of your scores might be lower than another for any of the reason mentioned above.
EDIT:
And as far as your question goes: No, I don't think you would be a good candidate for Amex with a FICO of 621. I would wait and get that number up to at least 700 across the board, and then apply for Amex Zync, which is their easiest card to obtain.
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EQ FAKO: 779 (03/26/15)
TU FAKO: 785(03/26/15)
Citi Double Cash | Citi Forward | BankAmericard Cash Rewards | Amex Zync
