For as long as i have been touring i have been pulling trailers. Two wheel, single wheel, big wheels, small wheels, drop out mount, frame mount, post mount, ETC always looking for the best solution to getting a little more stuff with me and maybe rolling a little faster than the last setup. I have pulled on and off road over some very big mountain passes, pulling over 100 pounds in gear. And yes i have destroyed a whole bunch of trailers over the years.
1 or 2 wheels??. This is a very easy question. There are many design advantages to both 1 and 2 wheeled trailers. On the road myself I prefer a two wheel trailer design as they tend to hold a better payload, and the design i use is good for a lot of things such as a cooking station, solar charging as the cargo box has a big top on it. I use a 700x40 tire and it handles some very rough roads, however it's limitations are quickly limited to zero when we hit a tight single track or an over grown double track. As far as tracking problems between one or two wheels i find it has more to do with the hitch mounting type and how strong, stiff and centered the Tough shaft is. For off road adventures i have found a single wheel has the best trail clearance and is way better thru rock gardens but lacks capacity in most cases.
What type of mount? there are a multitude of options here. Axle mount 1 or 2 sided seems to be the most used followed by frame side mounts and then post mounts. the most common trailer mount i see is the one side axle mount more or less works easy for everyone but has the least amount of manuverability an the worst tracking. Dual sided axel mount units inprove on the traking and handeling buy moving the pivot of the mount behind the wheel into a centered position allowing for truer tracking and better turning capabilities. Frame side mounts are a nice option on child cariers as an easy mounting option but have all of the same limitations of a single axle mount. Seat post mounted hitches are depending on the set up mounted to the seat post and reach over the rear tire this give a turning radius almost back on its self. This is mostly seen on heavy cargo or more expensive touring units.
I have my favorite setup as having both units. A two wheel with a set of 700x40 tire for the road that has a 55 gallon capacity. A single 29+ wheel trailer for off road adventures. My trailers are set up with a seat post mount and rack mount. bottom line on this is match what you use to best suit your needs.
Frenchman's lake, CA