My experience with Andrews FCU has actually been satisfactory ever since I joined them. I was one of the early adopters of that GlobeTrek card.
I went through all the things mentioned like faxing in a recent paycheck stub upon applying for it, but I made sure to get all of that done months in advance before going abroad. Don't know how much they streamlined their process since I joined, but reports say it has improved greatly.
As for the credit union itself and the card, I like it better than USAA. Andrews FCU members can do mobile and remote deposits, which USAA restricts said features to members of the military, and the credit card comes with 0% FTF as opposed to 1%.
It may not be "true" Chip-and-PIN, but it does have that capability on the CVM list, it even has offline Chip-and-PIN (plaintext verification) from what I see on cardpeek.
I can't speak for that card's usage in Europe, but it has worked fine for me in Canada, Mexico and Asia (Japan, Korea, Taiwan, Hong Kong, Singapore, Malaysia, Indonesia and Thailand) without any issues so far.