We and our children (now aged 4 and 1.5) moved from Lavender Hill to a much bigger house and garden, between Streatham Hill and Tulse Hill, last September. So far we'd definitely recommend it, we haven't looked back!
We quickly got used to the slightly longer commute (lots of train and buses, although from where we are most people seem to go to work by getting a bus down to Brixton and picking up the Victoria line there). It's true that the High Road is not incredibly charming but it has some lovely pockets and it improving every day. Everything seems better value here, not just houses but local groceries and even things like nail bars (if that's what interests you!). We find people very friendly and down to earth - our street is lovely, full of families who have really welcomed us. And small things like not having to worry about parking, have made life less stressful. It's also infinitely quieter than our old road.
As far as I can tell, most families seem to use the nearby local schools too which gives it a nice feeling. Our elder daughter has been in nursery at Hitherfield where she's flourished and has made some lovely friends so we're looking forward to her starting reception there. Other primary schools at this end that parents also seem keen on at this end are Streatham Wells, Julian's, and Henry Cavendish B (not saying others aren't great, those are just the ones I've heard most about). At secondary, most of the kids on our road go to Dunraven, which parents seem very happy with, or Elmgreen, also seems popular, the other side of Tulse Hill.
As I say, we haven't been here all that long but so far we're glad we made the move. I still miss SW11 when I'm back there, but can't imagine living there any more, lovely though it is. Feel free to message me if I can be more helpful.