You get what you pay for? In my experience, Toyota makes a very smooth automatic transmission. Yaris vs Aveo is probably not really a fair comparison. My wife's 2009 Yaris is a considerably better car than my 2010 Aveo IMO....but the Yaris used price was well over my Aveo new net price.

From the description you gave, it sounds like if there is a problem, it is suspension, not driveline related.