I think it depends on the quality of both the grammar and the independent.
An absolutely top flight independent can offer more than a grammar - the massive fees and highly able staff (not just academically able, but also in a range of other areas too which a state school just cannot afford to employ - eg top cricket coach) means a truly broad curri ulum of excellence can be offered.
The question is, will your child make use of the super duper opportunities or only those available in grammars or comps?
And will your child be at a top flivht indie or a more middling one which in reality migh not offer much more than the grammar in terms of curriculum, extra curriular or quality of staff.
It is hard to totally ignore the fees aspect because they are a key reason why the experience can differ so much. On an overall experience per £ I think the grammar must win. The question is whether you want to pay lots for the extras which my be very slight or significant depending on the indie in question.
I Actually think an indie can benefit a middling child most. Lots of indies will push and push and really force the best out of a child and get them to over perform of you like. That kind of child may not do so well in grammar with large classes and funding cuts.
Depends on the individual grammar, individual indie individual child, what the individual family wants and values most. Trouble is, when looking at these questions most people don't have perfect information especially about the schools, so its hard to decide.
For most, faced with a middling indie (and most are middling despite glossy brochure and sales pitch) and a child who can pass the state grammar exam for a good grammar, who aren't absolutely absolutely loaded, grammar is a good choice and the extras of indie are not worth it.....notice all the caveats.