I'm not sure about womens shoe sizing but in mens the Asics were true to size for me.
Some people are saying that if you have a very wide foot you might want to move up a half size. They also seem to think the Asics have a narrow toe box.
I just got my Asics and can tell you they fit me perfect. I ordered the same size as I do in other brands and there were no problems with the fit.
I also don't see the narrow toe box. I have a medium to slightly wide foot.
So, my advice would be to order the same size you always wear.