Personally I would look more at the method of instruction instead of whether it is competitive. I would find a place where the approach matches my kid's learning style.
I would agree. My DD HATES competition and would do very poorly in a highly competitive environment. She often withdraws when she feels she is being judged relative to others. However, when she has the opportunity to take on something unique and master it, she really thrives. One thing you might look at is whether "competitive" means individualized work with very high expectations for quality, or group work with competition for the "best" outcome (e.g. every student researches a topic of interest and presents it in a form of their choosing, vs. everyone writes a 3 page report and the "best" report goes on the bulletin board).
