I would app NFCU first. Barclays tends to get a little upset when you apply for new cards within 6 months of opening an account with them. I've heard countless stories of them doing AA, going as far as closing people's accounts for opening new accounts after them.
Barclays' inq sensitivity tends to be more about accounts opened after rather than before your app with them. If you get denied you can call up, they have one of the best recon departments out there.
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