I asked this question a few years back. I found that if you are getting proper voltage (like 120VAC), it is almost identical. However, if the CG's voltage is 110-115 volts, then there may be a performance difference.
I tend to leave mine on propane about 95% of the time. The 5% is when I have a generator running, so might as well have it set there. The propane use is about a quart (1 pound) a day.
As a performance helper, I would recommend some type of fan in the fridge and freezer. Valterra sells some small plastic fans that run for 4-6 weeks on a set of "D" batteries, and even though they move a small amount of air, it is good enough and helps noticeably.