TallFlyer: Omni picks people for classes based upon needs at the time of hiring. They will likely tell you which aircraft when they offer you a class date. Do not defer for another aircraft, as it could be months before another class. QOL is similar, however the 767 goes to more destinations. The 777 pilots more often run into landing currency issues due to heavy crewing and longer legs, but for the most part they do similar things. I believe they are both Polar qualified now.
Captjns: Yes, they would probably love your experience, however you can do better if you have that kind of time...