It's too bad that when it comes to towing,that it falls under the category of rocket science and manufacturers ratings with warranty,fall under the not true category.
Seems every time there is a, can I pull it with a 1/2 ton thread, power or lack of it comes up. A 6.0 or a 5.3 is just that, whether in a 1/2 ton or 3/4 ton and set up exactly the same, the 1/2 ton will have slightly more power because of weight.
My answer to the op is if that trailer is within the manufacturers ratings for towing, by all means use the 1500 and enjoy. If it's not then don't do it. Pretty simple.