I've not rode in an LS with standard shocks, so I can't tell you the difference. You've got a couple things to consider though. First, because of the springs you're using, they are a tighter, heavier spring... They have to be in order to allow for such a drop; if they weren't, you would be bottoming out near constantly. That's just how lowering springs work; they become tighter to better control/limit the suspension movement. SOOOOO... I can tell you that with my eibach's and my sport suspension, the ride is fine; it's a touch more firm than stock, but not bad. Now, with your Sprint's, which are bound to be a more firm spring; adding the sport shocks will obviously increase the firmness and give a harder ride than mine. To what extent... I don't know.
The sport shocks should however help out with excessive suspension articulation a bit if you're having a problem with that. They will dampen the movement of the car at a bit higher rate than standard shocks. But I would not expect anything significant in this department.
If you want handling, throw on the sport shocks and sway bars; I imagine with your car as low as it is, adding these things would really make it corner with the best of them.