Montessoris are very different from any other school type. I would not necessarily decide if your older boy really has attention issues just based on their say-so.
I do think some boys do better if they are a little older rather than younger. I volunteered each week last year in my first grader's class, and I could easily pick out the younger/later birthday kids (both boys and girls). And it wasn't based on their physical size.
The schools demand so much in today's world of sitting still and doing academic things at such an early age. Some kids are very bright intellectually but are emotionally at their chronological age, and the two don't mesh as well in early grades.