Neither of the two schools seem like a good option to me.
My dd attends a school for the highly gifted. This school is known for its rigorous curriculum and just like the school you mentioned the curriculum is for the most part 2 years ahead.
However, even there they only start doing homework in 2nd grade and only about 15 min per grade level. There isn't much testing or competition going on either, which is actually a little surprising to me. Kids work cooperatively and this is highly emphasized. When you have a group of HG-PG children in a classroom, there is no need to "push" them academically every single day as you described. To an outsider it may seem like the children are being "pushed" because the things they are doing are so far ahead of their age peers. I can assure you this is not always the case. These children are capable, without having to be pushed, of achieving higher/deeper levels in their day to day learning.
My dd is doing 4-6 grade math at age 7. I can assure you she is not stressed and probably finds her homework easier than most children doing math at their age level. Achievement testing done shows her at 7-8 grade level, so even here she is working way below what she is capable of. If she was in a regular classroom she would be stressed out and going out of her mind.
The most important thing to do is to find a good "match" for your child. Look at the children in the "highly gifted" school. Do they look happy? Are they engaged in the learning?
At the beginning of the school year I asked my dd how was school. Her answer:
"If I am dreaming, please don't wake me up"
That to me, is the perfect school.
