My only beef with the Aveo is the quality of the engine and transmission, and its lack of interior design and quality compared to the Rio or City.
As for build quality, that would really depend on where final assembly takes place. Build quality for the initial batches of Honda City vehicles was suspect because they're not direct from Japan, but like BlueBimmer says, this may have been solved with the facelift...
Kia Rios are all built in Korea, and build quality looks passably good. As for Aveos, Daewoo wasn't known for quality in construction or engineering when they died, and there's no word yet on how these new "Chevrolet" Daewoos hold up in the long-term. I wasn't particularly impressed with the plastics on the showroom models I've seen (but it's not as bad as the Chevy Spark), and I found it strange that on two Aveos in the showroom I visited, none of the plastic windshield moldings lined up with the panels, either... But at least the interiors don't seem any cheaper than Honda's or Kia's.
US Aveos may not be assembled in the same place as our local ones, but they're used to terrible build quality on domestic cars (that's asking for flames...
), so something as cheap as the Aveo that doesn't fall apart (and there, it's REALLY cheap) is bound to be well-accepted. And it does acceptably well there. Here? We're still getting over our paranoid fear of self-destructing Daewoos (ever wonder why a secondhand Espero costs even less than a Kia Pride?), so most people won't give the Aveo the benefit of the doubt.
Me? I think it's okay, but the Honda City is an exceptional car, and the Kia Rio is a more modern and better design. The Aveo is just simply... old.