Well, a lot. Stupid question. Both are slavery, yes, but chattel slavery in the US south was a special type and it really hurts modern slavery causes to equate them. Please stop doing this if you actually care about stopping modern slavery.
First off - when the prisoners have children, the prison doesn’t own that child. The child has an opportunity to stay with family. That’s markedly different. It’s not like generations of prisoners have been born in a prison, lived there their whole lives, and died on that same prison - that happened on plantations. It’s not like a prison can take your baby and bait alligators with it. They can’t force your child to help them bathe. They can’t rape your 15 year old sister, Sally Hemmings, and force her to act as Thomas Jefferson’s sex slave for decades.
Prisoners are allowed to read and write and practice their own religions. Prisoners are allowed to learn math.
There are laws meant to protect prisoners from brutality. At the time of antebellum slavery, while it was generally illegal to kill a slave needlessly, it was not illegal to beat or punish them and if they happened to die, that was not usually considered part of that law. LaLaurie in Louisiana is an example of someone who violated that law - it had to be particularly obscene and cruel (note that she was charged previously for cruelty to slaves, probably would have been charged for this, but fled mob justice).
Yes, I agree with you that it’s slavery and personally there’s a lot more slavery than that here (children are parents’ property). I agree that chattep slavery gave birth to this prison system slavery too. I don’t think it’s helpful to compare it to that specific type of slavery as if it’s the exact same.