Ok guys, I used my new HB classic today and I'm happy to say it works just as well as the Sport, shavewise.
The only real differences to me are the wheels, of course, as we all alluded to. They do make your glide smoother, but I found the (rear) pad on the classic makes you feel a bit more connected.
You do have to make sure you keep lubed as it will drag more.
The only other difference for me is I really like the grips on the classic much better, they give you a more controlled feel in my opinion. The unit itself works as well as the sport.
Blades are another story. The double that came with it had a tendency to really gunk up, and you had to be sure to rinse more often. I found it to drag the headslick along after a couple of strokes and not cut at all. This is not a big deal, since it is compatible with the Atra cartridges too.
I am going to try it with the triples for comparison.
Overall, I am glad I picked it up.
Now all I need is the Clear HB for a triple pronged arsenal!