RR,
It will improve your handling, but your satisfaction will depend how sensitive you are to it. Yes, I think you will feel a difference. It would turn crisper, flatter, and create a little more understeer with a front sway. Add a rear sway and it'll go back to neutral and be much flatter in harder turns. Include stiffer shocks and your handling will be even one more step crisper. Larger, wider rims with better tires takes you another step... The more steps you take, the less comfortable it will be on the street.. Sways are a good first step.

How necessary it is, is up to you. Sways, shocks, rims, tires, are not expensive steps, easy to install, and each one improves your handling. At some point consider front discs to stop you better. But that's more money.

EXAMPLE: I like to track race, so I put a 9lb FirmFeel tubular sway on the front of our '65, plus a rear sway.. plus stiffer shocks.. plus stickier, wider tires but stayed with 14" rims (Ford 6.5") to absorb harshness.. I have a very reasonably soft ride with much tighter, flatter handling than before..

- Art