It will depend on your children and the school. I went to a lovely 3-18 girls school, that my parents decided on when I was 18mths old (they picked it out for my older sister). It was, in my opinion, the best thing they ever did for me.
The school is (was?) supportive, kind, challenging and character building. Around the time I was 11 and progressing to the senior school, the school hit its academic stride and is now one of the top in my country (school is not in the uk, but "British Style").
However, I can't speak about the school your children will/would be attending. I suppose I could pm you the link to my old school if you want to compare it with the school you're considering (so you know where I'm coming from).
One thing I would mention- the extra expenses are hideous. For example, these were my "extras" for one term in Fifth Form (UK yr 11):
Netball Participation:£80
Netball Uniform: £110
Trip to Asia: £4100
Stockings (ripped, had to be replaced same day, accumulative): £20
Flights and Accommodation for Neuroscience competition: £135
Duke of Ed tramping trip: £34
Badminton Racket: £14
Maths Club Fee: £18
Music Lessons: £150
Winter Tie: £25
Exam Entrance Fee: £10
French Catch-Up Tuition: £85
Sports Registration Fee: £50
Fifth Form Camp: £340
Ski Trip: £220
Total (minus Asia trip): £1271
Grand Total: £5371
As you can see, for a 10 week term, that is one heck of a lot of money! That being said, extras don't get racked up at that rate until about Year 10 and that was an unusual term (hence why my family kept the statement of accounts). Usually, extras would cost about £250 a term + uniform items.
The work ethic you learn at a private school is astonishing. Many people claim children are spoon-fed at private schools, I believe this is not true. IME, when everyone around you is getting top grades, you push yourself until you achieve them as well. It sets you in good stead for university.
Are there kids there who don't do well? Yes
Are there bullies? Yes
Are there bad teachers? Yes
Are there leaky corridors? Yes
But...
Are there great exam results? Yes
Is there a good pastoral care and anti bullying system? Yes
Are there amazing teachers? Yes
Are there great facilities? Yes
Are there opportunities that other children simply don't have? Yes
Is it a better education than the local state school... ? In my case, yes it was (nearest state school 40 minutes away, anyway), in your families case, maybe not.
Investigate all your options before you pick and remember, you can always change schools.