This is you putting words in my mouth. It's bad if either wins.
You seem to be operating under an unspoken personal belief that an AI race "win" inevitably spills out into global dominance.
I don't know that it won't, but you likewise don't know that it will, and I'm not beholden to debate things from your chosen premise.
I think AI will be bad for whoever is being targeted by it's controllers, but I don't think it will intrinsically disrupt the military spheres that exist now as a result of nuclear weaponry.
China will use its AI to hurt the people it's hurting now.
The US will use its AI to hurt the people it's hurting now.
Imho, the idea of an AI arms race "winner" is just the new face of the securitization rhetoric that we used to justify our military excursionism during the Cold War.