If feel is an important factor for a player(as it is for many), your idea (two units) has a lot of value. Personally, my primary interest is focused squarely on the auditory element, though I realize I'm probably in the minority.
Nothing wrong with that -- what the audience hears is still the bottom line.
My first job as a teenager was working as a busboy at a Chinese restaurant. I remember the brothers who owned it telling me about the cooking academy in China where they learned. I was surprised to find out that "taste" wasn't the primary criteria for evaluating their food; in fact, it wasn't even in the top three: color, texture and aroma all came before taste. Most americans would probably put those criteria in a different order. But accepting that value-ordering for a minute, I think that for most players, tone is to guitar as color is to Chinese food. That "feel" I was talking about is like texture--not as big a deal as the tone, but an important criterion nonetheless.
Because for the audience, tone is probably like aroma, third in line after what notes you choose to play, how well you execute them, and how what you play works with what the other players are doing /what the song is going for.
So if my Axe FX tone onstage during a song is virtually identical to the Helix tone I'd get playing through my friend's rig,
but I get a subtle "feel" of interacting with an organic tube amp through the Fractal that I don't get through the Line 6, then I'm going to feel inspired in a slightly different way, leading to my choosing different things to play, and thus, upping the level of the most important element for the audience, my playing itself.
OK, I think I've talked myself into a plate of Shrimp with Lobster sauce...