A swaybar does basically three things:

1. Reduces body roll, which from a drivers perspective, often improves driver feel and confidence
2. Reducing roll can improve tire patch orientation IF it is excessive and/or not favorable to begin with, when cornering hard
3. It reduces total tire grip on that axle relative, to the improvement maybe gained in #2 above, by placing more load on one tire, and reducing tire loading on the other, which ALWAYS reduces that axles total grip. A swaybar never "equalizes" tire loading, quite the opposite, contrary to what many think.

#3 can be beneficial in that it might "balance" the two axles for improved driver "feel", but it is accomplished at the cost of tire grip.

Adding a rear bar is one way of reducing the effectiveness of an oversized the front bar.