I'm sad at people on here think that Boris Johnson is the way he is due to an Eton education. Boris was Boris before he ever spent a night there,
If your son has a shot at a fully financed education which includes required uniform and kit, I'd say explore the opportunity. Furthermore, Eton isn't the only interesting school in the UK and there are other more academic schools if you're looking Europe-wide. Depends what suits...
If successful, your son won't be the only child there being assisted financially by the school so if you're concerned about disparity, perhaps arrange to have a chat with another bursaried student when you visit; I'm sure they would be delighted to reflect on their own experience. I strongly suspect however that Eton will have that situation fully covered without prompting.
I would argue that being fair here means recognising and respecting the fact that your children are individuals and what suits one may be awful for the other.
You're not talking about whether to spend significant cash on one child and not on the other, this is soley about opportunity. Fairness is your support for an application to a school, which by bursary or by being a state option, is a result of the child's choice. So DS2 may not be Eton bursary material but precious few are. There are other schools who offer means-tested full bursary assistance and take the most able children. DS2 may however come through open days and decide he'd rather go to the local state school with his existing friends. Being fair is respecting that.
I went to public school and my sister chose local state school. We're still the sisters we were and most importantly, each of us recognises that we would have suffered in each other's schools. School experience, particularly a boarding experience, obviously shapes everyone, but blood is thicker than education.
Give yourself permission to follow up the opportunity if it's what your DS1 chooses and best of luck going forward. :)