I wish this topic had a poll, so I could view who's the most popular most quickly.
I believe the best girl companion was Dawn. Both May and Dawn were improvements from Misty, because they actively had goals, just like Ash. The way Misty became friends with Ash, however, was the most creative and meaningful. I think Misty would be the best to ship with Ash, yet that's not what makes her the best companion.
Whereas May's coordinator experience was a straightforward approach contests, which were eerily similar to trainer battles, Dawn's experience had more focus on making the pokemon shine, and finding ways to make their moves flashy. I felt as though May was held back by Max, because a large part of her character was showing how she was a good older sister figure. With Dawn, she goofed around and made mistakes a lot. Having Piplup as a humorous companion was so successful that this role carried on to Ash's Oshawott.
Iris is my favorite gymleader, and I like her video game character much more than Dawn. Yet unbiasedly, I felt as though Iris was a step back, because her goals of becoming a dragon master was focused in much fewer episodes. One improvement of Iris was how she was a jungle-raised girl, and how she was (slightly) less clichély girly.