With regards to the RSV feeling heavier it is because it is a little more top heavy, the HD has a lower center of gravity.
With regards to tires slipping in the curves, I suggest replacing them. The rubber gets hard with age and looses grip as a result, regardless of how much tread is still on the tire. I have fishtailed in corners because the last set of tires on my bike got too hard from age and even though they had lots of tread left it was not worth my hide to to continue using them.