I've rented Aveos, but they all had automatic transmissions of course so were horrible to drive.
I checked out the Nissan Versa, Honda Fit, and Toyota Yaris at an auto show, shortly after all three were introduced. I figured the trim falling the Versa was just normal wear-and-tear at an auto show -- but it wasn't falling off the other econoboxes that day.
IMO the Fit is probably the best of them (Aveo included) and better than the Hyundai and Kia models in that class. It costs more but you get what you pay for. The Versa has more interior room, but is ugly and cheap. The Yaris used to be the cheapest car in that class -- if the Versa is now the cheapest, it means Nissan is having trouble selling them and probably for good reasons.