Does it have to be either?
Barrett doesn't really support the commercial market, and just sold to an Australian company so likely even less commercial support going forward. Tough to get barrels, even though it's main selling feature is caliber conversions. That alone would make it a no from me.
Handle an AI before you consider buying one. Well built rifles that are well supported - easy to get barrels. However, the ergonomics may not be for you, the OEM trigger is only so-so, and the bolt lift is horrendously heavy. Despite what people say and what the AT-X was targeted for, AI's aren't comp guns (not that you said that's your goal for the rifle). Just something to keep in mind.
My vote is for a custom. However that's just my preference, it's a bit subjective of what people like and dislike in a rifle. If you know what features you like in a rifle, you can get the perfect rifle for YOU built.