I don't think any of us who are at the age to have children can take our experiences in school and match them up to what our children will experience. Yes, there are similarities, but the schools have changed, with standardization and the level of requirements to be met being pushed down a grade -aka kindergarten is the first grade of our experience (at least in traditional schools).
There is a stigma of being either the oldest or the youngest at to that point it is the individual child that points the parents to what they should do. And for that matter children can be tough in their honest assessment of others, and this is part of the task as parents we need to help them understand that everyone is coming from individual circumstances. As for thinking older children are stupid just because they older, it is something I will have to teach my son to address when he enters public school. As far as I can tell, being six at the start of kindergarten is a norm in our school district, and the practice of repeating kindergarten for close to cutoff age (esp boys) is common.
I have yet to come across a teacher or administrator who has suggested boys at the elementary level will thrive if they are close to school cutoff. As they get into the higher grades advanced placement classes can be used to keep them interested. I personally would rather the option of advancing if need be then holding back once they are part of an established grade level and have their cohorts.
To the original post, it would seem her son is currently struggling, and the change of school system cutoffs caused by the move has created the struggle. In this case it would seem best to me to let him catch up before moving him forward.