While I have not actually bred those breeds, I have lived next to a fighting operation for some years. Once the cock-fighting ban was enacted, my neighbors moved. I had gone over there several times just to look at the birds and had discussed several things with them.
They said:
1. The birds are naturally aggressive.
2. The birds were trained to not attack their owners.
3. The birds were trained to not run from other cocks (however, I'm not certain this is the case being that a bantam D'Uccle will take on a Standard Langshan cockerel...)
Whether these statements were true, or only true for this farm in particular, I cannot say. I will say that these birds never attacked their owners and were not aggressive towards their hens or children that were in the pens with them.
My ORIGINAL post was to let the original poster know that the Asil or any other breed, will not automatically be a fighting chicken. It may fight, like all birds will, but will not be the deadly killers they were once portrayed as. Some breeds are more aggressive than others. For instance...why the RIR was not considered a fighting bird I have YET to figure out. Those males can be mean suckers. But then, there are also very sweet cocks in that breed too.