My DDs have gone to Montessori for pre-primary and I really like the approach. Since we live in the "best" school district in the state, I couldn't justify the cost of private school beyond the preschool years, but would have if money were no object.
The big thing with Montessori is finding a good school with teachers that are properly trained. Unfortunately, since Montessori has become "trendy" and the name is in the public domain, any school can call itself Montessori. This has created a lot of confusion about what Montessori is. I've heard everything from it being wild and anything goes to ultra disciplined and pushing academics down kids throats. Neither would be true of a good Montessori school.
There are several core differences between Montessori and traditional classrooms. First, Montessori classrooms are multi-age. Generally it is 3-5; 1st-3rd; 4-6th. I find this to be a great benefit because there is continuity in the child's teacher and peers from year to year. It also keeps the class from "losing" the first month or so of school to figuring out the rules, etc. because every year 2/3 of the class already knows what's going on and the youngest students just entering naturally look to the older ones to model their behavior. Multi-age classrooms are also great for allowing kids to work at their own pace without getting tracked or labeled. It's just fine for a child to be doing "5th grade" reading work and "1st grade" math work when they are technically in second grade. Teachers should allow a child as much time as they need to master a skill and also keep presenting them with new material as they do, which means you should never run into a "sorry, our time for learning fractions is up, we're going to move on to place values now" or "yes, I know you've know everything in this text book, but you need to wait until next year before you move on" scenarios.
Montessori classes are also very holistic in how they approach learning skills. I'm not as familiar with the primary school education, but I do know that often they teach skills as part of larger projects. Rather than having strict math, reading, social studies, etc. units, there might be a unit on ancient Rome, where children work on geography, art, music, reading, and math as it relates to the topic. To me this makes learning much more interesting and relevant to kids and the skills they learn "stick" better because they are applied rather than just abstract.
Classrooms are generally self directed, which means that largely the child gets to choose what they want to work on. Here is where a lot of misconceptions about Montessori come in, and where the program can totally fall apart if the teachers aren't properly trained. A properly set up classroom will ensure that all of the choices the child has are learning opportunities. Nothing in a Montessori classroom won't have a specific purpose and teach multiple skills (even if the kids don't realize it). The classroom should also have defined spaces for the children to work (rugs, small tables and chairs, etc.) and every object or station should have a place where it can always be found and always returned. Also, the teachers need to be trained to observe the children and always know where they are in skill levels so that they can help them with new work and encourage them to move on to different areas if they are stagnating.
The biggest down sides I've heard to Montessori education is that the kids get used to having a great deal of freedom in the classroom (not to be confused with running wild, because the kids get to choose their work and define their own space you will generally find Montessori classes to be quieter and more orderly than normal ones). This can cause problems for some students when they move on to regular classrooms where things follow specific schedules. Another criticism I have heard is that students in Montessori classes tend to be academically ahead vs. the curriculum in traditional schools. I believe that this tends to be more acute in the lower grades, and as the kids get older the curve levels out.
The one obstacle I would see with your DS is that he doesn't have previous experience in Montessori. It can be hard to find a space in a program if you aren't entering either at the beginning of a cycle (age 6) or have gone through Montessori in the past.
The other "down side" I see is that you have to be OK with the idea that there generally aren't pre-determined milestones for measuring your child's progress. It is considered OK and favorable in a Montessori program for a child to choose to work on reading skills and ignore math for weeks at a time. They look at year long goals to be met and don't worry so much that they get equal parts of math/science/reading/etc. each day.
I don't think Montessori is a great fit for every type of child, but I do think the approach and philosophy mets the natural learning style of many children. Like any school program, look at the teachers, the facility, and your child and see if you think it is a good match for you.
Good luck!