It massively depends on the company (just as you can't really compare nursing with teaching or cartography with the OS or a job in the council finance department or a lifeguard at the local council pool.)
Is it a big or small company? Family run, franchise or big corporation? UK only or multinational?
What is the whole package? Salary, pension, private health, childcare vouchers, gym, company car... Last time I was in the public sector, I was offered a final salary pension, which is all very well, but when you're on a far lower salary than exactly the same role in the private sector might get, then it's not necessarily such a great deal. You need to do the maths.
Company policies on flexible working, parental leave, sick leave and so on can vary massively, so again, you need to look at what's officially offered, and try and find out from people currently working there how policy compares with practice. It may also vary departmentally within the same company, which may be because of managerial attitudes or the role - we have to have reception covered from 7am to 8pm, and their shifts reflect that, but in my department, we're not customer-facing, so there's a lot more flexibility on start and end times, and working from home when you're expecting deliveries or the car's in for a service or something. My employer has quite generous policies around sick pay and so on, but others will just go for the statutory minimum.
You can't just compare public and private sector, because there are far too many variables. You need to look at the details of what any particular employer offers. Some private sector employers are terrible, but others are really great, and probably a lot of them fall in the middle.