Lots of good picking above!
Bertram wrote: "... separate audio and video recording gives you more control over what you look like/sound like in either situation, but you have to sync them (i.e. you have to play the parts twice exactly the same way), ..."
Please pardon me for being dense, but I don't understand why you'd have to "play the parts twice exactly the same way".
Why not just have the video recorder and the audio recorder both running at the same time while playing?
I do that because my camcorder's built-in mic sucks, so I'll turn on the camcorder and also turn on the audio recorder (lately, a Zoom H2n) and let them both run simultaneously, while I'm trying to play something.
Then when I'm done recording, I remove both devices' SD memory cards and transfer the recordings to the laptop.
That does add double the complexity, because now for each part (whether melody, or backing, or harmony etc) you have 2 files to deal with (separate audio and video) instead of just video file with built-in audio, but sync isn't that hard because once you line up a few notes at the beginning of the tune, the rest of the tune will be in sync all the way through (assuming no issues with software or YouTube rendering misbehavior).
Maybe I'm just doing it very simple-mindedly. I don't do any cutting and splicing or whatever it's called, and I play mostly oldtime style stuff where each instrument plays basically from start to finish of each tune. Not much to it. I suppose it would be more tedious for bluegrass or complicated arrangements where they have all the solo 'break' parts to deal with.
An aside: I wouldn't be able to play something exactly the same way twice anyhow, as I use too many variations each time through and I have no clue what exactly I'm doing. Guess that means I'd be useless at creating slick Hollywood 'lip-sync' videos with overdubbed 'corrections' etc. Oh well! Don't want to anyway. Lol.