I've posted on this before. There is a huge spectrum of "Montessori" for schools. We were in a full-on, AMI Montessori school for my 2 gifted boys for 2 years. We were really unimpressed and moved to our public school.
The negatives to a "real" Montessori school:
1) Tends to have huge class sizes. My son's class had 36 kids with one teacher and 2 "helpers," who were not allowed to teach the lessons.
2) The child must get taught the lesson and then repeats it on their own. If they already know the lesson, they still have to do it, and do it "the Montessori way." That can be very boring for a gifted and/or creative child.
3) Frequently not alot of writing. Not alot of "traditional" topics like history, social studies, or hard science.
4) No accountability- no homework, no tests. Although that sounds great, how do you know that your child has learned what they are supposed to learn? It's a huge leap of faith on your part.
I will say that the math can be fantastic. My kids started exposure to multiplication and long division at age 4. My older one in first grade tested at 5th grade for math, partly due to Montessori.
Both my kids were bored silly by the Montessori. I realized how many deficits the curriculum had, and I ended up teaching them things afterschool to compensate.