It totally depends on where you live and what the elementary schools near you are like! I am assuming cost is not a factor for you, as obviously private school will be much more expensive than public.
When you say 'private' school- that can be SO many different things! If you are religious and your husband specifically wants a religious component such as a Jewish, Catholic, Lutheran, etc. education, then you should start looking at different schools in your denomination in your area. Don;t just go with the closest one- check out several!
Even so- it might not be the best fit!For example, my fiancee went to a Montessori school as a young child and has really fond memories of that early experience. But in high school he attended a very prestigious private Catholic school (he was very bright and his family wanted him to get a really great education) - and although he got excellent grades, he hated it and has NO friends from those early days.The atmosphere there was one of bullying and favoritism and he insists that he would never send any child of his to that school, although it achieves high marks academically.
I went to a public school, got excellent grades and am still friends with people from 1st grade on. Did he get a better education than I did? Possibly, but we both went to the college of our choice, so its all relative, right?
Or you could be looking for a different school experience, such as Montessori school or the Waldorf method of education. All of these approaches can be really great- but they are not all going to always be the best fit for YOUR child. You need to educate yourselves about the different methods and how they work and how YOUR child interacts and learns and try and get a good match.
On the other hand, depending on where you are, public school can be great. We moved where we are specifically so my son could attend his public school, which is ranked as one of the best elementary schools in the state and has about 300 kids in it. Public schools in our area score very high all the way through high school, which is also something to consider. If you are in the city and the public school nearest you is not one you want your child to attend, you can try and get her into a magnet school, but it is a lottery system, so you might not get what you want.
Do some research on ALL the school options in your neighborhood. Look online at Greatschools.com and see what people say. Talk to parents you know with older kids and see what they say about their experiences at local schools. Call the principals at schools in your area and arrange to tour the school. What are YOUR priorities? Art & music and extras? Strong math and science? It all depends...
You don't say why your husband wants private school- but that is just not always a guarantee of a great school or a good fit for your child. Talk seriously with him about why he feels that way and what his priorities are. Then do some research together and see which schools appeal to both of you.
I have to agree with the comment below- there are 'bad crowds' everywhere!! Lots of private schools have plenty of bad apples. Don't be naive and assume that your kid will never run across one in a religious or private school. Your daughter will mix with all sorts of kids at ANY school and in her neighborhood- its part of life!!Good luck!