Good idea to check the eTrailer listings; they are often very helpful. In this case, they show the same Curt, plus the equivalent Tow-Ready. There are multiple versions to suit the different connectors of the LED and incandescent lights. Both brands plug in to the factory connectors, so there is no tapping of wires, which is good. Both brands have powered converters so they don't overload the car's lighting circuits, which is good. After a brief look, there doesn't seem to be much difference between brands.
The wiring for the lights should work out fine. Now what about brakes?
Rocketball - how heavy will your trailer be, does it have brakes, and if so what kind are they? If you have electric trailer brakes, this lighting wiring will work, but you will need to add more wiring for the brakes.
Kedis82ZE8 - I see that your trailer only weighs 850 pounds empty, but presumably it will be much heavier when loaded... so it should have brakes. It looks like your wiring doesn't support electric trailer brakes; do you have surge brakes on the trailer?