I have worked 4 on 4 off, 4 on 2 off and 6 on 3 off in my time and I much prefer working 4x4 12 hour shifts. Once you have been there 8 it isn't that much further to get to 12! 4 on 2 off was the worst pattern I have worked as you only manage to get a weekend off every 6 weeks!
My 12 hour shift pattern was 4 days then 4 off then sometimes 4 nights or 4 days again. In the day there were 2 controllers on but only 1 at night which for us meant fewer night shifts so always a bonus.
I would not like to work the 2 days 2 nights pattern as it means you are always doing night shifts every shift run which I think is a lot more fatiguing than doing 4, your body has time to adjust, and then having a gap where you only do day shifts. At worst it means you have 12 days between night shifts.
Now I have moved to a Big Airline I am now doing Monday to Fridays, oh how I wish for 4 on 4 off again!!