Whatever you get will be a huge improvement.
Not familiar with that particular brand. The one we bought eleven years ago is about the same size at 4'x6', and one of the most used tools we have. The King Kutter looks to have a longer tongue which could make backing much easier. The height is comfortable for minimal back bending when loading/unloading. The payload is pleasingly useable. I'm sure I've come close to or exceeded the 2,000 pound rating a time or two when hauling oak rounds. With a trailer of this size, trailer brakes may be a considerable factor in your choice. Our trailer has electric brakes on one axle but I've never really noticed them in use with our flat ground. I did not find any mention of brakes on the King Kutter. Our quad is under six hundred pounds, and the foot print per square inch would be pretty light for controlling a loaded trailer on a slope.
Another possible option is a four wheel nursery wagon. The thing with that is it doesn't follow like a tandem axle, and I can't back it up more than ten feet on a really good day. The Kory 3000 we have does not have brakes either. The deck is 4'x8' and the payload is 3,000 pounds. Both trailers have wheel bearings and substantial tires, which of course, is more expensive initially, and arguably less expensive in the long run. As I said previously, our trailer is elven years old, and the replacement cost is now double or more the initial $1,100. purchase price.
I added a tongue jack early on, and recently replaced all the wiring, and the brake backing plate assembly. I bought new drums for the brake axle but they did not fit due to the off set in the new hubs for the bearing placement and the castle nut would not screw on far enough for the cotter key. The Thule has an electric actuator used for dumping. The wiring can be, and has been a maintenance issue. For several years the in frame wiring, and quad to trailer connector plugs chaffed and failed. The hydraulic hand pump on the King Kutter may be more reliable long term.
The tandem axle has a fairly small foot print. We back it in the garage once winter sets in, to stage a weeks worth of wood for the wood stove (5th photo).
An after thought is the tailgate. Ours has spring loaded pins top and bottom, which makes it easily removable for dumping, and equally convenient to unpin the top and hang it down when loading heavy items like rounds.