From my experience;
The teaching standards are far greater at the elite private schools compared to any selective-entry school. Most teachers at selective-entry are average, some are really good, whilst some are really really bad.
The biggest advantage of going to a selective-entry school in my opinion is the environment. You are surrounded by 100s of extremely hard working classmates. So if you have difficulty in any question/topic etc. you don't necessarily have to rely on your teacher, you'll have many classmates to help you out. The environment itself will really motivate you to study and achieve - when you are in an environment where most people are striving and working hard - you'd want to do the same.
Also I reckon going to a select-entry school myself taught me how to independently learn, something that's been useful for me in my university studies. IDK how it's like in private schools but apparently you are spoon fed everything and then the transition from school to uni is difficult because in uni you're own your own.
All the best