As far as I can see, Moderna started earlier (in the US), focussed on the US (unlike AZ) and have been quicker in their study to get the data to the FDA.
Speculation but ... AZ had a guaranteed 100M doses with the UK if it worked (plus however many in the EU), so maybe this made more sense for them to focus here?
There has also been some "comment" in the US on the original data, so it probably makes sense for them to have a pretty robust and US-only data set before submission.
I worked in an industry connected with drug approvals. It's not so much that they are better in the US, but if you haven't got everything in place 100% consistent with their system first time, then you can make your life very difficult.
I wouldn't be 100% surprised if the FDA didn't approve the Oxford-AZ vaccine first time.