There is functionally no difference, in terms of added harmonics, between turning the instrument's volume up to 10 and turning the input level on the amp sim down to taste, versus adjusting the instrument volume to determine the amount of overdrive you get. The amplifier or amp sim won't know the difference.
However, standard gain-staging principles normally call for a hot signal coming in, for a better signal-to-noise ratio. You're also lowering the output impedance of the instrument when you turn the volume knob down, which can have a small effect on tone. Keeping the volume at 100% also eliminates any noise that might be added by the potentiometer itself (even a clean one), since it's essentially out of the circuit.
So I guess my vote would be for 10, at least as the default starting point, using the input gain on the amp or amp sim to adjust the incoming level. I'm open to being proved wrong via an audio demo, but I believe there will be no tonal difference between adjusting one versus the other as long as the level hitting the distortion algorithm ends up the same.
However, it's much easier to tweak the level with your pinky finger while playing than it is to reach over and grab the mouse. The recorded part may not call for flat-out distortion from beginning to end. The guitar's controls really are there for a reason, which is to accommodate dynamic changes as you play.
The tone knob, though, that's a matter of taste. It's going to determine what frequencies the amp or amp sim adds harmonics to. Turning the tone control down will give a different effect than using a low-pass filter after the amp sim, because it's limiting what frequencies are presented to the amp sim to be distorted. Turning it up presents the full spectrum to the amp sim, increasing the percentage of higher harmonics and thus changing their distribution.
My own preference is taking the capacitor out of the circuit by turning the tone knob all the way up on the guitar, and using a filter at the input of the amp sim instead. But then, I am not a guitarist! Subtlety on the guitar, for me, is something I add later through automation. :)