My wife and I (mostly my wife) home schooled our son through 5th grade and then transitioned him to a private school. My wife and I are both college educated, I have a job that pays well enough that my wife does not need to work outside the home and as such has chosen to be a home wife/mom.
The main drawbacks to home schooling that we encountered were...
1) It's a lot of work, the parent doing the schooling should consider it their job. If that parent also needs/wants to work outside the home I would find it difficult to recommend home schooling.
2) There is some expense (but a lot less than the private school he attends now).
3) It gets harder as they get older and the material become more difficult. My wife (who is not a math person) had no difficulty teaching all of the math up through 5th grade, but now that he is doing algebra, helping with math homework is something that falls to me.
4) Ignorant people wondered if we were in some sort of cult and were attempting to teach our son that the earth is flat, or that he would become some sort of sociopath because they figure we probably just lock him in a closet with a pile of text books.
The benefits that we enjoyed were...
1) Massive flexibility, during my son's 4th grade year he was studying American history so we incorporated a 4-week trip to the east coast into his program for the year. He was able to see in person many of the famous historical locations that he had, up to that point, only read about. My son probably did 10 times as many field trips by the end of 5th grade as I did in my entire 13 years of public K-12 education.
2) Class size, in every education funding debate I hear, one of the biggest things that teacher's are always asking for is a lower student:teacher ratio. Homeschooling is the absolute sweet spot there, the student teacher ratio in our home school was 1:1.
3) Tailored lesson plans, our son's teacher was the person in the world who knows his strengths & weaknesses the best. I don't think I can overstate this, no teacher will ever know your kids as well as you do or be able to customize the way they instruct them to the same degree. For example when he was younger our son had some vision issues that required special glasses and vision therapy, this caused him to struggle with reading. My wife was able to compensate for this by using more audio book in his lessons while we worked through the reading issues. I think it's pretty likely that without this ability to fit the teaching style to his needs he would have struggled badly in a typical classroom.
4) How many traditional schools let you come to class in your pajamas?
A couple other thoughts...
1) People often wonder why you would want to do yourself that a professional educator has been extensively trained to do. I think this sort of misses the mark, my wife and I were not doing what a professional teacher does (manage a classroom full of kids from many different family backgrounds with very different individual strengths/weaknesses and do it on a very tight schedule).
2) There are TONs of groups supporting home schoolers (at least in our area). There are several great Co-ops where kids can sign up for classes in area that parents feel they are not equipped to teach (e.g. our son was able to take classes like Archery and Robotics at the co-op that would not have been available at a traditional elementary school.
In the end I think the decision will depend a lot on your personal circumstances, if you don't feel good about your local public schools and cannot afford private school then home schooling is worth considering. Are your kids well outside the norms (either above or below) in some areas, if so then home schooling will allow you do adapt their education to help them catch up or allow them to excel. How does your wife get along with your kids? If they already butt heads over many things then making her mom and teacher may not be the best plan; as our son approached the teen years it was more and more difficult for her to act as both mom and teacher and that was a factor in our change from home school to traditional school.
That's my $0.02 worth.