If you do end up working for NATS you could be at a unit with under 20 controllers, or you could be at one of the centers with hundreds. These workplaces will have different shift patterns and different pros and cons.
In general I find that I have a lot of time off now compared to when I worked 9-5, however a lot of it is when most people are working. I generally enjoy this as it means I can do my shopping when nobody else is there, I can go to the gym when it's quiet etc. Also it means I spend almost no time in the rush-hour traffic unlike many others.
The downside as said above is that you can't have weekly activities the way many do, although it's not impossible to attend most of them. I have collegues who try to avoid afternoonshifts in order to attend evening-activities, this means they tend to work 4 mornings and 2 nights. At the unit where I work this is often possible, but it depends on your collegues and your workplace.
Would I go back to 9-5? No, the pros for me well outweigh the cons. I would suggest if you're interested that you apply and see how it goes, statistically you will most likely not get in anyway (harsh I know, but those are the numbers) but if you do it's (I think) a great job.