I was once driving a 883 on the streets of south Bali, it was really nice to ride and I loved it. Great rumble, they don't care about mufflers much there, anyway ... and a nice overall experience.
But they have these tiny little Ninja 250's (about 30hp) there, and fact is that they were much quicker.
It depends on the type of street and the rider of course, but IMHO an 883 is just not a bike to compare or mess with a Rocket. It is best when one rides it at low speeds, like maybe 40-80 kph.
A 1200 kit alone will not change that, one would have to completely mod the bike and exchange most of the critical parts, basically turn the whole machine into something else.
But why do that? A Sportster is nice, being just what it is. I'd love to rumble along the beach with it, again. Cannot bring the Rocket anyway, if I go there...