My findings:
I need to start by saying there must be plenty of people out there who are better at round filing than I am, since I only chisel file my own chains.
I have a saw on the bench waiting for a new top end on which I'll do some mild porting. Figured I'd work on the guy's chain while I'm waiting for the jug and for another saw that didn't show up this morning.
It's a Stihl round-ground chisel chain that's pretty dull but not a nightmare. I have it locked in a chain vise for filing. The file I'm using is a Finnish file with the little castle on it. Out-to-in filing is natural enough for me after decades of chisel filing and I sometimes even file my gullets out-to-in to remove or minimize a burr. (Gullets are typically round filed on chisel-ground chains, just to hawg out material.)
Round filing this Stihl chain, out-to-in, I'm still getting a tiny burr (that I can barely feel but not see, even when magnified) on the top plate and down in the gullet, but MUCH less than filing in-to-out. Not at all surprising. As you probably already know, the round file does want to chatter and squawk a bit more than when in-to-out filing.
Next time I get an Oregon chain that needs round filing, I'll do the same and let you know if there is any substantive difference from how the Stihl chain is turning out.
Something you may want to try is out-to-in if it's just a light touch up. If you need to whittle a lot off as I'm doing, you could try in-to-out for most of the chewing and then finish it up with out-to-in to remove most of the burr and get it a little sharper.
I doubt my $0.02 amounts to much at the current inflation rate.