I've installed Avast, left AVG on the machine but "switched on", and everything seems much the same, as you'd expect.
It looks as if Avast doesn't do a nightly scan of the whole computer, which AVG did, but if the incoming protection is working, that shouldn't be needed anyway.
You should uninstall one of them. They won't run happily together. If you run into problems, run full uninstalls on both, use the removal tools. (Disconnect from the internerd. And the Avast uninstall tool is
here. (AVG's is at post 10.)
It's true Avast doesn't run scheduled scans, that's the downside of the free version. I consider that downside minor. They could have (like some other makers) reduced some other functionality. Like detection rate/cleaning ability. I'd run a manual scan once a month or so. The first time you do this, you'll be a bit bewildered. Any malware found, the scan will stop, waiting for you to tell it what to do. There's lots of advice about this at the Avast forum.