Fees aside....

My decision - in a world where money was no object - would be based entirely on the individual merits of the two schools in question. My experience (across eight children who've attended over the past sixteen years) is of a super selective grammar which is not and never has been an exam factor and has worked very well for a parent like myself who prefers to stand right back and let the teachers do the teaching. sendsummer sounds a very wise cautionary note about the effect of financial implications for provision, but the ethos of a school and its leadership is vastly more important, ultimately, in a pupil's experience, than issues of funding. That said, grammars, along with the whole of the state sector, are squeezed and that will make itself felt in certain less popular subjects being cut and certainly in the ability of a school to offer four subjects at KS5. I agree that the EPQ is a cheap option. Not without merit but there's no doubt that part of its appeal to state schools is the low cost of rolling it out.

The main reason for a grammar school would be shorter days (including possibly no Saturday school) leaving more flexibility for time consuming outside activities. However if your DS would like activities within school day then the independent usually suits better.
I am not convinced by the super selective grammars are exam factories argument. I think some selective independent schools are just as much exam factories (in that their reputation depends on exam results) but masked by a glossier package. Other independent schools do really deliver extra to the syllabus. I don't count EPQs which are a cheap way for sixth forms to get extra points for their pupils and for certain school league tables.
Grammar schools will have less funds for activities and teaching certain subjects and parents may have to be more involved to compensate for the lack of resources.

It depends on the grammar and the independent. You should get smaller classes at the independent and the big pull for us, aside from boarding, was the fact that at the independent DD would get a chance to have a go at what she wanted to do and would not be selected out. The grammar was 1300 Girls, the independent was 450.

There were more very bright girls at the grammar but I had heard the competitive parents for years going on and on about how their worlds would collapse if their DCs didn’t get a place it just seemed best for us to leave them to it. The girls grammar is outstanding and results were comparable.

DD had huge opportunities at her school and grasped them. She wasn’t sporty but she spent a term at a school in South Africa and did a lot of music at school as well as drama and House competitions. It was a truly rounded and broad education. We didn’t regret it. DD has the job she always wanted and school gave her the confidence to go for it.

It really depends. I know inEssex lots of parents who could afford fees would instead send their children to the Grammars if they got in. (But if they didn’t would pay to give them the next best chance.)

Language choices
School trips
How far people travel to each school - some have a wide geographic spread

We made the decision based on facilities, class sizes and distance

Surely it depends on the respective schools. Grammars are not all the same. Selective Independents are not all the same.

If the academic level is the same, it's down to your DC's personality and how well you think they would fit in to school - ethos, pastoral care, co-curricular opportunities.

Also availability of subject options, willingness to run courses even when take up is only a handful of pupils. Availability of equipment and materials, number of practical lab sessions

Convenience of school run.

I guess it how you define normal

It all depends which grammar you're talking about. There's a massive difference between a "normal" grammar in a "normal" town, as opposed to some super selective in a leafy millionaire area of Kent.

"More "normal" range of pupils?
I guess it how you define normal

We chose a super selective big name full boarding school over a top 5 super selective grammar (day). Logistics i.e. travelling aside which was a big issue for us, I felt the grammar was an exam factory and I just didn't like its ethos and that the boarding school offered a much broader curriculum (fairly obviously they have the time and resources to do this) and I loved its ethos. Last year through work I was at the grammar for a couple of days I was right it is an exam factory and I I hated the ethos!
My DS isn't overly sporty and is certainly not a team sports player but he was exposed to things at his boarding school that the grammar never could with all the good will in the world. He's very science/math orientated but this exposure meant he took art and science based subject for Pre U (A level equivalent). I think if he'd gone to the grammar he would have become a science nerd.

also preferred the staff at the boarding school very relaxed and informal and most of the parents they like me are totally hands off. I found the parents at the super selective grammar scary (and I'm not easily scared) ambition was bristling out of their every pore.

More "normal" range of pupils?