The R6 is a dedicated single-purpose sportbike. Like a racing bike with license plates. It's really made for track days, not for the street. It sacrifices everything for speed and handling. It has a small, hard seat, because you get some feedback through your butt. It has an extreme seating position that puts stress on your wrists and lower back. It has a high-performance engine with a narrow powerband, so you have to keep it revved up close to the redline to get the power out of it. It has very sensitive steering geometry, almost twitchy.
The YZF is more general-purpose, it's not a dedicated sportbike, it's a 'sporty' bike. Better seat, more comfortable position, wider powerband (though basically the same engine, I think), etc. So if you want to go camping for a weekend you won't feel all bent up like a pretzel after 30 min. A better bike for learning to ride because the steering is gentler and more forgiving. And probably safer because it's not made to push the envelope.