We have experience with pulling (& backing) 1, 2, & 3 axle trailers.
As far as backing, the 1 axle trailer is really squirrel-ly ie it tends to cut faster & quicker than a 2 axle & sometimes seems to have a mind of its own.
There is not much difference between the 2 (31') & 3 (34') axle trailers, although there is a slight advantage to the 3 axle as when you back up, it tracks a bit better than the 2 axle. The 3 axle trailer is very civilized when backing up, provided you have the room
A lot depends on the style of hitch that you have as well - we've found that the hensley allows for a sharper angle when backing into tight spots. As well, if you have a receiver on the front as per Andy's suggestion, you can control a 2 axle better than a single axle.