You can't really directly compare the acquisition of English and American Sign Language to the development of two spoken languages.
Because they're languages in different modalities.
I have access to American Sign language, for example, but not to spoken English.
In order to use English I need an interpreter, or read lips, or the information has to be available in written form.
Children who have two deaf parents, and lots of children with one hearing and one deaf parent as well, acquire both sign language and spoken language.
My children know I don't have access to spoken language, and that they need to use sign language to communicate with me.
That's different from the acquistion of two spoken languages.
Some parents say their child uses more spoken language once he's been to school.
I don't see that in my children. I see them developing positively and using both languages.
This might be a different situation than when a child has to acquire two spoken languages, but I haven't seen any research into this yet.