It massively depends on what you're doing, I suspect. What sort of job, and what size employer and so on.
I've done exactly the same techy job (unix sys admin) for the private sector (large multinationals) and public sector. Pay for that in the private sector with that sort of employer is about double what I was on in the public sector, but I am quite well-paid for what I do; I could get even more, were I prepared to work in the City, but I could also be on quite a bit less if I were working for a smaller private sector employer. I'd probably also have fewer benefits and training and so on, but it really does depend on the employer. Maternity pay and so on is more generous than statutory.
In the government agency I worked for, I had formal flexible working, but I have effective flexible working where I currently am, and can work from home more easily, which also adds flexibility. I did have a final salary pension in my last job, but when it's based on a rubbish salary, that doesn't seem much of a benefit; people on other salaries in other positions might see things differently - length of service also counts, and I think not long after I left, they closed the final salary scheme to new entrants anyway.
One of the things I love about working for multinationals is that I get to talk to people all round the world every day - in comparison, I found the government agency rather parochial. They were all lovely people, but the buzz isn't the same. I like walking down the corridor and hearing all sorts of different languages. Some people hate it, I know.
I think looking at it from a public/private split is mostly a waste of time. You need to work out what's important to you (maternity pay may not be an issue, if you've got older children and aren't intending to increase your family, for example, but flexible working arrangements might be, for example.) You need to look at the conditions, pay and benefits offered for a particular job, the size of the organisation, where the job is based (my job would feel very different if I were based in one of the small field offices than in the large European HQ), holiday entitlement, the commute and so on. If you can, find out from people who are there currently how it feels - experiences vary between departments and the management people experience at that level. I would definitely recommend people to work for my company, but I really wouldn't recommend working in my department until they sort out a particular management issue by sacking the useless, bullying git.