The capability of both vehicles will be borderline identical, differentiated only by the minor weight differences.
Compare the official tow capacity for a 2008 LX570 and 2008 LC 200 - both are at 8500lbs. At some point later, both capacities were officially decreased, the LC 200 to around 8200lbs, and the LX570 to 7000lbs. As I understand it, these were done due to changes in regulartions/laws, not due to any changes of the vehicles themselves. The 2014 models still have identical engines, brakes, transmissions, frames, tow hitches, suspension, etc. Identical vehicles, but now rated differently.
The biggest difference is AHC in the LX, which is a huge win for towing. It supports heavy tongue weights much better than static (traditional) suspension, and will self-level the vehicle once the trailer has been attached. This improves handling, towing dynamics, weight distribution, etc.
If your primary goal for a new vehicle is towing, a 3/4 or 1-ton truck may be a better option than either 200 series. But that said, a 4000-4500lb trailer will be a joke of a task for both the LC and the LX. Beyond weight, consider the physical size of the trailer, the towing setup, weight distribution, etc. A very long trailer would not be a good match for the LC/LX due to its relatively short wheelbase, but a heavier yer shorter trailer may be just fine. Lots of variables at play.