Very different frame and suspension. Most of the trailer hitches for both flavors of ST use the muffler mounts for the horizontal hoop on the hitch and then a "hanger" or riser runs up to the best solid point that can be found under the seat on the rear sub-frame. I have some very detail photos of my hitch install on the ST1100, that is similar to the ST1300, but you have to be a member on that forum to see them.
I have been inspecting the CTX1300 frame for mounting points for a hitch thinking I may have to build my own. I have a Mini-Mate camper that I pulled with the ST1100 and am considering if I want to pull it with the CTX.
See my gallery here for those photos. You might get enough of a look at the hitch too.
A much better, more stable hitch on both those bikes is the style similar to the design made for a UniGo trailer, or Bushtec trailer, and I've seen a few custom made by owner versions for the ST. All are VERY different mounting than what I had on my GW.