There is no single answer to this question. Let us examine all the pros and cons of each.
Uniaxial trailer cottage.
Pros. All trailers up to 7 meters long are now only made single-axle. This is due to the fact that two-axle trailers in Europe are subject to increased road tax. And if the length of your train is more than 12 meters, the road tax will be even more. It is also worth more and place on the ferry.
Uniaxial trailers have less rolling resistance and better maneuverability.
Minuses. All the main disadvantages of a one-way trailer add up because of our "directions". Strong vertical buildup. The trailer cottage loves to jump in the pits and hummocks and try to swing around its only axis (especially if the length of the trailer is under 7 meters). You may not feel this if your tractor truck weighs more than two tons, but if you have a small or mid-size passenger car, the rear passengers on the bumps will be thrown like a herring in a can.
The loads that could not be swallowed, not intended for Russia, by a torsion bar suspension, are transferred to furniture, which soon begins to move away from the walls, and the walls themselves in turn from the floor. In the sad case of excessive loads, you may crack the frame in the area of the trailer axle.
Two-axle trailer cottage.
Pros. Significantly free from problems with single-axle trailers in terms of vertical swings and furniture damage. Axis two and around them swing much more difficult. Also, the patch of contact with the road is much larger and you still need to look for a hole into which the trailer will hit both wheels at once. Hence, a smoother course and greater energy intensity of the suspensions (there are two of them too), and as a result, a reduction of vibrations harmful to furniture.
Large load capacity. If you can load 50-70 kg into a single-axle trailer, then 100-150 kg are already in a two-axle trailer.
If it so happened that you pierced one wheel, but you do not have a spare one, then you can easily get to the place of tire mounting on three (after removing the punctured wheel from the hub).
Just a big capacity. And this is also very important.
Minuses. The disadvantages are also related to Europe, in which you need to pay an increased road tax for a two-axle trailer.
Because all two-axle trailers have a length of 7 meters and are heavy enough, you will need the category "BE" in the rights. By the way, all the same it is better for you to open it (and this is done fairly not difficult and not expensive), so that the valiant servants of the law would not detain you with long conversations "but how is it really correct."
Slightly more drag when rolling with a similar uniaxial trailer, which of course you will not notice.
Larger sizes require more responsible management, especially when maneuvering in cramped conditions.
Summarizing, you can refer to the following:
If you take an auto-trailer for traveling around Europe with its beautiful roads, then you should opt for a single-axle trailer.
If you plan to travel around Mother Russia and not only in the Moscow region, as well as if you have a big family and you want to stay in one place for a long time, you should opt for a two-axle trailer.