If we were the kind who place bets on things such as this (we aren't), we would put our money on the Sonic to achieve better real-world mileage.
The Aveo, last sold for the 2011 model year, was a more basic subcompact than the Sonic, and it came with a 1.6-liter engine and a choice of a five-speed manual transmission with EPA estimates of 27/35 mpg city/highway or a four-speed automatic rated for 25/34 mpg.
In comparison, the Sonic 1.8-liter has EPA estimates of 26/35 mpg with a five-speed manual and 25/35 mpg with a six-speed automatic. The Sonic 1.4-liter tops that with EPA ratings of 29/40 mpg with a six-speed manual and 27/37 mpg with a six-speed automatic.
Having more transmission gears doesn't always translate into higher mileage, but we think it would in this case because the transmissions are hitched to newer, more efficient engines.
A Sonic with the 1.8-liter engine and six-speed automatic that competed in our $16,000 Subcompact Shootout averaged 30 mpg from a mix of city and urban-expressway driving. In a different test, a Chevrolet Cruze with the 1.4-liter averaged 33.2 mpg despite carrying an additional 400 pounds compared with the Sonic.
Though we can't say for sure, we doubt that an Aveo could match the mileage of either the Sonic or the Cruze if driven under similar conditions.