In my experience, it was always easier to close a girl with a warm approach. I think it is like the “chode way” of pulling a girl. This is because you feel more entitled to speak with the girl and to become physical more quickly. Vice versa a girl does not judge you if you know her and be cocky, physical with her and she can rationalize it easier in front of her female friends. Otherwise she would have to explain it and if you are too uncalibrated she feels like a slut.
Cold approach is the best way of learning this shit, how you can make a girl feel awesome in your presence. This needs a lot of practice and calibration, as well as nuts and bolts. You are indeed needy in the girls eyes if you do not give her excuses why it is okay in front of her friends to be so physical with a previous stranger, i.e. rationalization of the women (see the Michael metaphor of Julien).
If you are able to make the HB and her friends feel awesome with you they think you are the coolest guy in the world. Moreover you have infinite amount of girls to approach, instead just making warm approaches in your small social circle.
A nice way in my experience is to merge the girls. Play a funny game, introduce your sets to each other, saying “hey meet my girlfriend”, “Hey meet my cousin”, “hey meet my friend”,… This is field tested. It works like awesome shit. And it is fucking simple. The girls are raising their buying temperatures while talking to each other, and are so excited to meet your sister, … This gives you a shit load of value.
Other ways might being just expressive, being funny. If you know funny stories, have no filters and say what is in your mind. You become sympathetic very soon, i.e. reaching the social hook point. Afterwards you have enough value to choose your girl of the group. Know they can justify to being physical with you. Because she know you have a high value, and their friends too. That the best justification and the best source of attraction for a girl.