In general, the stiffer rear will cause the car to rotate quicker. Basically, it's reducing understeer, or if you look at it from the other side, increasing oversteer. This isn't necessarily a bad thing.
Oversteer is when you hit the wall with the back of the car first. Understeer is when you hit the wall with the front of the car first.
Almost every car on the road is set up by default with a lot of push (understeer) because someone somewhere thought it was safer. If you feel like you're coming around too quickly, you can change the rear bar to compensate. A softer bar (or shock, or spring) will keep the rear from coming around as quickly. Stiffening the front will do the same. The trick is figuring out where the problem actually is. Sometimes your adjustability is only on one side, so you have to fix everything from there and it doesn't matter where the problem is.
Considering you're purchasing springs and dampers, get adjustable bars as well so you can tune it in to your taste. It's likely to be a bit quicker to rotate than you're used to, so give it a few days, maybe a week, and get used to the feel. Another option is to get adjustable dampers, although that may be more expensive.
-Michael