Mine were both, primarily my Mother and it is really made a difference to the way I bring DD up. Although she is just 2 I make a conscious effort to encourage her to try new things, new experiences and mingle with lots of different people; I think it has built her confidence as like I was she is inclined to be shy and a deep thinker and a worrier. I was kept in a bit of a bubble until school.
I am also aware that in her teenage years I want to show trust and give her more freedom that I was, as having such overbearing untrusting parents did mess me up during these years. Having said this I don't want to be too relaxed about things like BF sleeping over and drinking that kind of thing. It's hard.
Would like to hear if anyone else has the same mentality...