To me, there only seems to be disadvantages. I'm cross lateral/dominant, so I'm right handed, but left eye dominant. I remember reading it's good to keep your power hand (mostly the right hand for people) in the back because then the dominant eye (right eye) is in the back as well. Having the dominant eye in line with your power hand in the back would make your cross more accurate. And plus, it won't get injured as much since the dominant eye isn't in the front. However, for people like me, I wonder if I'm at a disadvantage since I'm cross dominant. Since I'm left eye dominant, should I just switch to southpaw, which I am somewhat comfortable in, despite my left hand being weaker? Also, do you know any well accomplished boxers who are cross dominant like me?
I'm the same (natural righty, left eye dominant) but I fight southpaw most of the time, my left was okay naturally but not as strong as my right, worked on my left from different positions and it's my stronger hand now. Training out of both stances helps to feel what's working and what's not, when you spar experiment and see what feels best for you. I guarantee that there would be many top boxers who have the same deal as you or me, it's not much of an issue and it's said to be an advantage for sprinters due to balance benefits so don't worry about it, just do what is comfortable.