I am also regional "flotsam" enjoying the superior QOL (and dining, even with the limitations of the crew meal system- sure beats running to Asian Chao or BK in 20 minute turns) at NetJets for for over a year now. It is far, far from perfect but much, much better than life ever was for me at the regionals.
As far as 7 days on goes, for me it "feels" about the same as an airline 5-day, which is to say it feels long and never-ending, but not nearly as long as if I had a "7-day trip" at an airline. I used to be a commuter and had things like back to back 3-days which seemed longer than a NJ 7day tour.
The more relaxed and measured pace compared to the constant hub-and-spoke quick turns, plus the mystery and variety of not knowing what is in store from day to day, for me anyhow, is what has this moderating effect. And by and large things have a way of evening out between busy multi-leg days, hotel sits, and "assuming the position" in an FBO lounge chair during some long turns. (Those lounges by and large are a lot more comfy than sitting in a departure lounge at ops for 4 hour 50 minute no-hotel-room turns at LGA or whatever with the regionals.)
As to the domicile system for new hires- silly, and hopefully one day it will go away. For now it is a big con, obviously.
In a nutshell, for me-- plenty of pros, some cons, but the pros outweigh the cons by a good margin.