Agreed with the other points.... if this move to Ohio is a short term stint - I would stick with BA due to lounge access on strictly domestic trips with AA.

Even if his stay in Ohio is longer term or permanent, I would play out the BA status game for a year or two to see if the marginal benefits of aforementioned lounge access on domestic trips as well as accruals towards lifetime status with BA are worth it.

If his travel continues to be Int'l Biz heavy, the lounge access angle is pretty moot and a switch to AA could be beneficial from the earning of redeemable AA miles aspect. Especially if the road to LT status over at BA is more than a few years out.

If more domestic legs in the US are going to be present in his travel patterns, a switch to AA would be a plus for IRROPS protection and the general ease of being part of AAdvantage while residing in US and flying AA.

So, stick with BA for a year or two and then evaluate a change to AA if it makes sense!