My son and I just completed 4000 miles from Portland ME to Portland OR. We made the decision to use Burley Nomad trailers vs panniers. I our opinion it was by far the best way to pack and go cross country.
First, it allowed us to use our standard bikes. We didn't have anything on our bikes, everything was packed in the trailers. As a result, our bikes handled like they typically did, not stability or balance issues.
Second, you really don't notice the trailers from a maneuvering perspective. You have to recognize they are behind you and watch out on really narrow shoulders or weaving in traffic, but other than that, you don't even know they are there. No down hill stability issues (we went over 40 mph with our trailers). Braking wasn't a problem even down 6% grades in the rain.
Third, they hold so much and packing is a breeze. We carried our back packs in the trailers along with tents and sleeping bags. When we finished a ride, we would get groceries and carry them in the trailers. Our heaviest load (lot of extra water and snacks for lunch) was when we climbed to Powder River pass in the Big Horns at ~9700 ft, 35 miles of climbing and the trailers were a non issue. They were great on the decent to Tensleep at roughly 40 mph.
They are not totally waterproof, but will prevent things from getting wet except in a complete downpour. They have a lot of side pockets for storing things. We brought an extra tire, hitch and hitch latching mechanism, just in case. Didn't need the hitch or hitch latching mechanism, but we did get a lot of flats, you might want a kevlar tire. I would recommend these trailers for any long distance ride.
One other item to mention, the trailers made it easy for my son an I to bring our full size laptops that we used every night for rout planning and blogging (RideWithGPS).