Secondary teacher.
A few things:
You can progress quickly, I'm a career changer and I'm Head of Dept in my 4th year of teaching. As someone else has pointed out, though, sometimes it's luck of the draw, I was in the right place at the right time. That said, I do have a First, a Masters (in my subject) and years of experience, so being the right person also helped progression.
Teachers pay - London have a significant uplift, i.e. around + £7k per spine point on main scale and this widens on the upper scale to +£11k. In other words, you have to consider where you are in the country when looking at pay.
Pensions: the Teachers Pension Scheme is good, however, a useful rule of thumb is that you contribute about 10% and the employer about 30%. So that person on £51k is actually paying £425 into their pension every month. A fair few private schools aren't enrolled in the Teachers Pension Scheme which would mean the advantages for retirement and death in services cover aren't as good.
On the flipside, a lot of private schools offer reduced fees for children of staff. That could be a big benefit for you.
Although I have no experience of private, my understanding is that extra-curricular is compulsory for most staff - days are long. There's also the added complication that parents are paying for a service and the assumption is that many want that service to include good results and a guaranteed career trajectory. I believe this will likely add to workload.
Bursaries for retraining: available for sciences and maths at secondary. These core subjects mean that you'll probably find yourself teaching classes with no aptitude, so you'll find yourself endlessly 'adapting' resources to ensure they pass. Obviously, that would be different if it were an exam entry private.
I could never teach primary. I wouldn't want to deal with 30 kids day-in-day-out who are busily developing attachment disorders. Too much interpersonal stuff for me. I have my own family. I don't need a work family.
OK, so honest appraisal. My experience doesn't match most of the people who are struggling. This is despite working in state, in a deprived area, and joining a school in Special Measures straight out of PGCE. We're now rated Good. Some of that is definitely down to me (hence the rapid promotion) and a decent head / leadership team.
In terms of workload, yeah, I don't get these people who are doing it 24/7. Years of management experience, in both the public and private sector, mean that I have a lot of transferrable skills. For example, you mention 'analysis'. I can do this standing on my head. I enjoyed making the QLA (question level analysis) for recent mock results. I know how to get it to spit out the data I need to use for targeted intervention. And I'm not at all phased by the idea that our papers will go for external moderation because two years ago I figured out that I'd need to be an exam marker for the relevant board so I've had all that training and my grades are bullet proof. Meanwhile, I know of another department in another school who cocked up their mock analysis, gave the kids all the wrong grades, don't have any meaningful intervention plans, completely lack marking experience, and are now being carpeted - frankly, as they should be.
The other thing about workload is autonomy. 1265 in state schools, where the employers are tied to the 'Burgundy Book,' means you can only be 'directed' for 1265 hours every school year - works out at something like 32.5 hours pw. No teacher can get their work done within this timeframe (see a previous post of mine on this board about a colleague who was insistent she wasn't going to work more than 32.5 hours pw), so the rest falls under some amorphous statement about 'and any other reasonable additional hours'. The thing is, they can't tell you where or when to do these 'reasonable additional hours' and the only things that can be required of you in this time are planning, prep and assessment. In other words, all this extra work people are talking about being forced to do by management, I don't know what it is. Sure, as HOD I have to lead a department and this can come down to producing general admin stuff, and I'm responsible for ensuring we having a working curriculum, but I can do these tasks where and when I want. I just don't get how I'm putting in a 40-45 hour week while other general classroom teachers seem to be saying 60-70 hours. And I teach humanities, so the marking load is horrendous. Anyway, point being, state schools with strong unions are good for being able to push back on workload. It's more tricky in private schools who aren't tied to the 'Burgundy Book'.
My school isn't lovely, as mentioned above, it's in a very deprived area (bottom 10% nationally in terms of income), majority white working class (not very aspirational) and roughly half the kids in every class are SEN. That said, I don't have many behaviour issues in my classroom, and by behaviour issues I mean any sort of disruption that interferes with teaching. To be honest, I couldn't 100% tell you why. I think it's related to the years of work experience and an understanding of firm boundaries. I don't believe it's solely a school culture thing because other teachers have really big challenges with exactly the same classes.
Anyway, I've probably said enough to get me torn to shreds. But my experience, as a career changer, i.e. someone with decades of experience managing resources (including people), is that teaching is kind of OK. The kids make me laugh every day, I have a lot of job satisfaction, I sleep well, I eat well, I go out and have holidays. If I'm honest, the biggest issues I face are either from sub-30 y/o teachers or those who have only ever been teachers. Both struggle as they haven't built up the skills or experience that would make their jobs so much easier.