Do not know particulars of this area...but the academic gains made by sending kids to Head Start Programs, overall, are short lived. By second grade...I believe, if I remember correctly, the "head start" is gone. But, individually, a family, or the kids may benefit otherwise.
Do not be concerned about "socialization" or socializing skills of your kids, if you stay at home with them. See Gordon Neufeld's book (avail at library) Hold Onto Your Kids; Why Parents Should Matter More Than Peers.
A child psych in Canada with 35 years experience talks about the dangers of putting any kids or adolescents together for long periods of time without intense adult care and guidance. Kids of the same age do NOT teach each other skills that get them ahead...emotionally, academically, socially etc. That is why we have terrible problems in this country with bullying. Kids always establish a pecking order. Adults may not see it, but it is there...and it is stressful..for those at the top, to maintain, and those at the bottom, to survive, and those in the middle, to figure out where they are.
Staying with a loving, caring adult who can focus nearly one-on-one attention on them, a child has a much better chance of keeping self-esteem, and eventually finding maturity. This is one reason colleges are favoring home schooled kids...they really can think independently, and do not fall-in-with the crowd so easily.
I think you would have to have a rough or dysfunctional home life for a government program to beat the personal attention you give your child. If you are SAHM...and plan to keep it that way, I'd skip it.
I am not just someone in love with a relatively new book...I am a public school teacher, and have lived overseas in other cultures, and have seen how true Neufeld's observations are...highly recommend reading it...I can not cover all that he touches on here.
I am not saying the teachers or programs in daycare preschool or Head Start are poor...it is just impossible to replicate the individualized home care you can provide, in a class setting. Yes, kids who go to such programs may also seem to have more social skills or be better able to sit and follow directions etc, but at what price? I, and others ask. And for how long? There is lots of info available to read.