I (personally) would rather blur the lines between friendship and authority and have my children trust me completely, than risk alienating them when they need me the most.
From what I see in raising my children (poorly, as we all must), the balance you want is "authority without oppression". e.g. "I'm the leader on this road trip of life, and I'm actively training you to take over every responsibility you're capable of" as opposed to, say, "I'm the leader so SIT DOWN."
Being a "buddy" (Tiger Mom / Kitten Dad) gives your children no one to rely on when the life hits the fan.
Obviously I can't say for sure that had my parents done X, I would have done Y, but their lack of any attempt to connect with my siblings and I on any meaningful level has had a massive impact. I don't hold a grudge against either of them but there are certainly things I know now should have raised major red flags and they completely missed them. Still, that goes deeper than whether or not I could consider them a "friend"!
I don't really think that's what my child needs from me. We can be buddies _at times_ but overall he looks up to me for help, advice and guidance on a very different level than his BFF. Both types of relationship are crucial but I don't think it my role to meet every bonding need of my child - some things just don't mix well.