Slightly different scenario than what you're asking about, but here's my experience. I went to one of the top GATE public high schools in NYC for my first two years of high school. I switched to an international school for my junior and senior years after my family moved abroad for a job. Looking back, it was a good thing. The academics at the GATE school were generally good, and I had friends, but it was a massive school (~700 per grade) and felt somewhat anonymous. For some teachers, I was just another name on a Delaney card. The international school was far from GATE, as they took kids at all levels. But they had a decent IB/AP program, and it was much smaller (~100 per grade). My teachers and my guidance counselor knew me, they knew my parents, and the classes were smaller. I didn't realize it at the time, but I did so much better in a less crowded environment, and went on to a small liberal arts college instead of a large university.

For some kids, a top-rated GATE school is not necessarily better than a decent non-GATE school.