or stiffer anything in the rear will cause oversteer because it sends roll (and thus weight and grip) to the front.
A stiffer front end will reduce grip in the front and increase it in the back.
You might get more grip on the end with the extra roll stiffness if it reduces camber loss due to roll, in which case your total grip (and thus available cornering force) will go up, but it will still change the handling balance the same way. If you use really big sway bars to compensate for a bad camber curve you end up with a car which gets snappy and unpredictable at the limit, especially at higher speeds.
IMHO anti-roll bars are highly misunderstood and commonly used to mask other more serious handling problems. Ideally you would want no sway bars at all.