Differing parenting techniques causing rift between girlfriend and i?

I had my daughter when i was 16 but i was lucky that i had a great support system at home. My daughter was brought up in a very liberal household. Now that she is approaching the same age i was when i had her, my girlfriend has become very possessive of her. She never says it but i know that she looks down on me for having her so young. They're both very close and my daughter respects her a lot, however my girlfriends parenting technique is in direct opposition to mine. My daughter can go wherever she wants as long as she is back by 8pm on a school night and usually 10pm on weekends. She usually tells me where she is, but i'm not prepared to guarantee anything as she is young and neither she nor i are perfect. I want my girlfriend to give her a break. Last night she wanted to attend a party at her friends and my girlfriend didn't allow it although it was a saturday night. She's going to push her away and that is where the danger lies in my eyes. Am i too lenient or is my girlfriend too