A lot of people here will disagree with me, but I can only relate my first-hand experience. I've come to the conclusion that if your TT is properly balanced and has a properly set up hitch, sway is a non-issue.
I've towed mine (7100 lbs loaded, 30' bumper to ball) over 65,000 miles including over high bridges, though high-wind areas, and across the Sierra in light snow and slushy roads. I've run my Equal-I-Zer hitch on dry bars and with lightly lubricated bars (which is supposed to kill any sway control effect) and noticed no difference in handling. I've never experienced anything approaching sway in the sense of a cyclic lateral instability. Ninety-nine percent of the time I wouldn't even know that my trailer was back there save for the additional inertia on acceleration and braking. The bow wave of a passing truck or bus does give me a slight momentary push, but nothing that would come close to moving me out of my lane unless I was completely asleep at the wheel.
I've never towed a fiver, and I can understand why those can be even more stable than my TT, but "more stable" would for me probably be a distinction without a difference.
My daughter tows a 2,700 lb (loaded weight) popup with a V6 Kia Sorento. No sway control or WD hitch. She also is careful to balance its tongue weight and ball height to keep it towing level. I've driven it, and it also is stable and beautifully behaved on the road.
Again, there are a lot of folks here who will disagree with me, but I'm only relating my personal experience. Be smart about tow vehicle selection (Short story: Don't push the published limits) and tongue weight loading and don't let the scaremongers bother you away from a TT just for fear of sway. There are better reasons to choose a fiver (or TT) than that.
As for a cap, I assume you're thinking of some aerodynamic stabilizing benefit. I have no experience with that, one way or the other.
But a cap does let you put stuff in the truck bed, which can be nice since most TTs have limited storage compared with fivers. Just keep in mind that all stuff has weight, and everything in any part of your truck counts against its payload weight, axle weights, and GCW, (gross combined weight) so that storage space isn't free.