A girl is walking and you want to talk to her. What do you do? The two choices you have present two distinct problems.

A girl that is walking usually is trying to get somewhere. Stopping her in this context is dumb.

Walking with a girl presents a different problem: possibly making her feel like she is being followed.

Whats the better choice? I would definitely say walking with her. It is the most natural thing, and it shouldn't feel weird if you are slightly ahead of her as you talk. Eventually as the conversation opens you can move more to being side to side as you walk. It also becomes safer to stop her.