Single axle trailers are by far the most popular of the two options. There are a variety of different reasons why they are universally more popular. Firstly they are going to come at a lower cost, due to the smaller size and less complicated construction they can be a lot less expensive than double axle trailers. Only two wheels, tyres and sets of bearings, means less parts that can potentially be damaged. This means maintenance costs will also be lower in the long run. Another cost factor is that the smaller size makes single axle trailers more economical to tow. In all single axle trailers are going to be cheaper overall than double axle trailers.
Another benefit of single axle trailers is that they are easier to tow and will be easier to manoeuvre. This means for easy odd jobs and so on it can be easier to get around in areas that are more constricted.
Now we have gone over the bigger benefits of single axle trailers what are the cons? Due to their smaller size you are not going to be able to tow as much cargo with a single axle trailer. Tyres on single axle trailers do have a tendency to wear out more quickly than double axle trailers. This is due to the fact that you only have two tyres to spread the weight across rather than two.