I have one and use it for grocery shopping. I only got it this spring, so can't speak for durability, so far so good.
As far as turning goes, it tracks behind beautifully, you barely even know it's there. I only noticed that I needed to take a little wider turn on a few occasions, usually I just ride as normal.
It doesn't feel that wide, I think it would compare to a width of a bike with packed panniers.
You could add some reflective tape to the sides, if you're concerned about cars.
Overall I'm very happy with my purchase.
Since you got one, take it for a test ride. Best way to find out if you like it.
Brompton M6R, Salsa Mukluk II, Trek 7500, Raliegh fixie, 3 SS cruisers, JC Higgins Color Flow, Junker Flying Jet, KHS F20-A, Worksman trike
I don't own a Burley Travoy but I built one just like it using a golf caddy bag I found at a thrift store for less than $5, and I also made a full-sized DIY bike trailer. Between a full-sized trailer and the Travoy-style trailer, the Travoy-style is much easier to tow. Both corner well, but the shorter length of the Travoy-style trailer definitely has a smaller turning radius than a full-sized trailer.
Between the two types, the Travoy-style is definitely a more care-free towing experience. If all you are going to be hauling smaller loads like when commuting or going for a small amount of groceries, the Travoy-style is probably the way to go. If you do a lot of hauling, like to go car free a lot, or have to get groceries for the entire family, a larger trailer would be better.
In terms of width, the Travoy-style trailer is still not as wide as a full set of rear panniers.
Here is my DIY Travoy-style trailer in action. Because it isn't nearly as long as a full-style trailer, its smaller profile takes the corners better.