Ok. A long response. Hopefully even handed! I don't want a pile on. Please remember experiences will differ, this is mine.
I'll start by saying I think both are good schools, and you're lucky to have the choice.
It really depends what you're looking for. The reason Rutherford is seen as "academic" is more to do with the class/demographic of the families that choose it, rather than the education the children receive. Many of the leavers go on to private secondary schools, but be under no illusions that this is a reflection of what the school does. This is, in many cases, achieved by extensive tutoring at KS2, funded by parents who can afford the sessions, and ultimately, to pay the fees. The school set homework, but there is no pressure to do it, and no rigour when it comes to marking. The school is very popular, and some of the classes have over 30 children in it. This is great for finding friends in the class, but not always so great in terms of pupil:teacher ratio. I don't get the sense they would be able/willing to nurture talent just in the school. They simply don't have the staff/time. And with the school now full, you really feel the lack of actual space in the building.
The headmistress is extremely hard working, and passionate about her school. She works crazy hours, and goes above and beyond when motivated to do so. However, the senior management team seems top heavy, and communication isn't always the best. I've never been sure who deals with what (very possibly my bad!), and emails/messages are often ignored. The headmistress once actually told my husband "I don't read emails". Things can seem quite chaotic, and I get the feeling that the staff don't always get fully behind the senior management team. The class teachers are good, but they are mainly young and inexperienced, and staff turnover is high. This is probably not unusual for London primary schools, and the kids jog on with it. In my experience, the teachers with a few more years under their belts can deal with it all a bit better.
The Friends are very active, and they are always keen to do events that bring together the community, and help raise money for the school. And the Fairs and Quiz nights etc are great fun. I've made some great parent friends by attending these sort of events. If you want your child to try lots of different activities, the after school clubs are really varied, and I don't think any other school locally (free or private) comes close to what they can offer. And the sports department are very ambitious with tournaments/matches against other schools.
So, why did we move our youngest to Ravenstone? When we were choosing a school in 2015, and went round it, I would have described it as chaotic. They had just had a very negative OFSTED report, the then Headmaster was winding down to retire, and the place really needed an injection of energy. Fortunately, they got that in spades with Joe Croft, the current headmaster. He couldn't have been 30 when he took over (in 2016? It was definitely after we applied for schools). He is just one of those rare people who exudes leadership. He is dynamic and approachable, and the staff seem to genuinely be behind him. When there has been any kind of question/problem, it is dealt with swiftly.
The child:teacher ratio seems much better in the more senior years (think it's bulkier in the early years), and that gives the teachers and LSAs (who are generally more mature and experienced) more time to give each child some individual attention. This has been really important to us, our child has SEN, and we always felt he was a burden at Rutherford (potentially messing up their stats), but he is seen as an individual at Ravenstone. I always used to emerge from Parent consultations at Rutherford with a sense of hopelessness and despair. That hasn't yet been the case at Ravenstone.
The club provision isn't as strong and varied, but there are options, and it's a much simpler process where you deal direct with the provider (not all clubs at Rutherford can satisfy the demand).
The demographic is much broader, and the school has a great community feel. The events I've attended so far seem well run and popular. And, of course, there are also children who will go on to fee paying/selective schools, but probably fewer who try/want to.
I don't know if that's been in any way helpful? Hope so. And as I said at the start, they are both great. Happy to answer any specific questions of comparison if I can.
Best of luck, and welcome to Balham x