Most non-XR7 1983-88 Cougars did not come with a rear sway bar. Those that did (some V8 models) had a pitifully small one. And the front bar, while thick, can be improved upon. To make handling much better you can add (or change to) thicker sway bars. In conjunction with the 15:1 steering rack, a thicker front sway bar and larger rear bar will absolutely plant your butt in the seat during aggressive cornering. You'll wonder how you ever drove without them. These bars will give your cornering the best bang for the buck and should be one of the first things you change in your front end.
For the front, the XR7/Turbo Coupe bar will work (any year, 1983-88). Or, you may use one from a 1987-93 Mustang 5.0 only, as they are the same part as the XR7/TC. You can usually find good, used sway bars easily at salvage yards or swap meets, or even online via eBay or Rock Auto.
Don't forget about the end links. Traditionally you would never even give them a second thought until one of them breaks. However, replacing them with new, thicker links will make a big difference. And be sure to get kits with urethane bushings. In fact, make sure the sway bar main bushings are urethane as well. That is the best way to take all of the sloppiness out of the front end, and you will simply not believe the difference in handling with the addition of the new bar and all urethane bushings.
For the rear, the Turbo Coupe/XR7/Mustang bar works here as well. If you're using aftermarket lower control arms, the location of the sway bar mounts is somewhat different than stock, meaning your sway bar will be lower to the ground and closer to the rear differential (pumpkin) cover. Be sure that you'll have enough clearance while you drive. If the car is not lowered, you should not have any ground clearance problems with the relocated sway bar.
There are companies that make aftermarket sway bars. Most are lighter in weight, and some are set up specifically for drag racing, meaning that they'll be less effective during cornering. There are even adjustable ones. The Ford pieces are definitely more plentiful and more affordable, that's for sure, and coupled to a urethane bushing kit, they'll hold up against anything out there. It just all depends on your driving habits, and what you need for your specific intentions (road racing, drag strip, etc.). For normal street driving, the OEM-type thicker bars are more than adequate.