Aseels are supposed to smarter and more tactical. Even though they are slow, they are strategic and know how to hit a predator where it hurts, based on what I have read.
I honestly don't know. What knowledge I have of the breed is mainly from a guy in the village who keeps them. I hope to have a breeding pair from him next year.
His (the guy in the village) has already killed two of the cats they had and he doesn't worry about weasels which are common here.
Granted Mink, assuming we are talking about the large black American mink that we are unfortunate enough to have here as an invasive species have the reputation of being deadly.
I'm not condoning any of what I write below but the Aseels here are essentially fighting cocks. The man my friend got the Aseels from used to fight them. It's illegal here now but people still do it.
Centrarchid may well be right and their reputation may have been 'talked up'. I know an Aseel can kill a weasel because people here have put both in a cage and let them fight.
One person might be exaggerating but I've heard such stories from a number of people I consider reliable.
For the OP I still think an important factor is how the rooster was kept. There are very few free ranging here. Most are kept in runs.
In India where the breed is more common, this may not be the case. The mentality of a caged fighting cock and a free ranging cock with a female I would expect to be rather different. This is the common wisdom here.
I think the saying 'it's not the dog in the fight that matters, it's the fight in the dog' may be relevant here.
Whatever the reputation and the real capabilities I would still advise the OP against getting an Aseel cock hoping it will defend his flock against Mink. Far better imo to deal with the Mink.