What is the ideal relationship between parents and children? This relationship should be more severe, parents imposing their terms automatically, or should it be a friendship? In the latter case, if the child benefit from parents' indulgence and do something stupid? I know that the situation varies from case to case, but I speak in general. My husband and I get ready to be parents again, we want to adopt for the first time, and therefore we want more opinions. So, what do you think?

authoritative parenting is generaly considered the best.  it is a mix of the two exaples you gave. 

http://www.athealth.com/Practitioner/ceduc/parentingstyles.html
http://parenting.families.com/blog/authoritative-parenting-an-overview
http://www.extension.umn.edu/specializations/familydevelopment/authpar.html
http://childparenting.about.com/od/parentingeducation/a/authoritative.htm
http://en.wikipedia.org/wiki/Parenting_styles
http://findarticles.com/p/articles/mi_qa3614/is_200110/ai_n8958286/
http://parenthood.library.wisc.edu/Larzelere/Larzelere.html
http://www.pasadenaisd.org/ParentUniversity/parent11.htm

i applaud you for adopting. adopting a child can be incredably fulfilling