I think it really depends on what makes you and your family happy.
I grew up in a not very great area of London, and went to quite a rough secondary school. I am sure my primary school was not great either but I was young enough to have only good memories of this and being told off! I was a teenager in London and it sucked until I went to college when I then spent a lot of time clubbing etc with my friends, but that involved a lot of night travel by public transport in order to do this. I did not do that many activities (sport etc) although funnily enough I did sailing.
I moved to the south west as a young adult and would not consider returning to London, especially now I have a family.
The positives for me certainly are:
Access to the beach, daily if I chose, within a 20 min drive, access to the sea within a 10 minute walk
Access to the countryside within a 20 min drive max, the moors, woods, open space.
Access to watersports - a must for me.
Schooling - the schools are smaller here, I beleive anyway, certainly at primary level. I am sure there are problems at primary here as well as in London, but the severity of inner city problems are not so prominant where I live (although still a city so has its share).
It is easier to find a nice area to live that is not overun by deprived areas.
Accommodation is cheaper
There is plenty to do activity wise, in particular outdoor pursuits for the children as they grow older.
You don't have to travel so far to go on holiday in beautiful locations! [biased emoticon]
Negatives:
Work can be difficult to come by, especially if in certain professions
Wages are lower - this is probably the biggest negative of living in the south west.
Culturally less diverse
Night life is not as good as in London - less options for theatre, art galleries etc (but you can go back to London to visit those), clubs shut early.
Depending on where you chose to live, you might have to travel to take your children to school and there might be less options for secondary schools.