I don't believe they should be treated any differently. But I was very involved in the Irish-American community for a few years and it was my experience that the difference between Irish illegals and Mexican border criminals is that the Irish just come for a couple of years and then go back.
Of all the Irish guys I knew, only a couple of them stayed.
The Mexicans, on the other hand, come and stay. They never bother to learn the language or assimilate. They just come to collect welfare and turn our country into the same armpit they just left.
Most of the Irish guys I knew just came over to work for a couple of years, make a little money, party, and then go back. To all the ones I knew, it was more like an extended Spring Break than actual immigration.
So, while they're both illegal and they should both be prosecuted, I don't have contempt for the Irish the way I do for the Mexicans, because I know the Irish aren't doing it to be malicious.