See i was going to say the opposite because I don't see why intellectual ability isn't like any other talent
If eldest dc was incredibly good at football and offered a place at a football academy would you say no because it wasn't fair on his brother? How about if he was incredibly talented musically and offered a place at a conservatory? What if he was a good actor and won a role in a film, would you deny him that opportunity?
Conversely, if one if them was disabled and were offered special opportunities because of that would you reject it because it wasn't fair on their sibling?
What if there was a bigger age gap and you'd accepted the private place before it became apparent the youngest one wasn't at the same level - would you have made the eldest then drop out half way through his education?
Where does it end? If one of them goes to uni and one doesn't, do you refuse to help out the one who does, despite the epectation parents earning too much for their children to qualify for the full loan do so, because you aren't giving the same amount to their sibling.
Treating them fairly doesn't mean treating them equally and exactly the same, because they are not exactly the same people.
Youngest might resent you if eldest gets a better education than him but equally eldest might very well resent not being given a life altering opportunity just because his brother might not get it.
The only fair way is to allow them both to apply and then whether they get in or not is on their own merits. Exactly as if they both wanted to be in their local football team or auditioned for an orchestra etc.