You can experience poor towing characteristics from either if they are not properly hitched or truck is undersized. We tow a similar sized TT that scales a bit over 10K# with our 3/4 ton HD crewcab Silverado and enjoy a very comfortable ride while towing.
Dealer did a pretty good job installing our WD/SC hitch but after I did some minor tweaking we can tow at interstate speeds with virtually no sway even when passing diesel commercial trucks. Gets pretty windy in our neck of the woods and we rarely have any issues with towing comfort when going down the road.
For long heavy TTs such as what you are considering having a truck that is capable of handling that load is paramount to success. You can use a high-end hitch (Hensley/Propride) but they are not required if you have ample truck. Our Reese WD hitch with integrated SC works well for our current towing combination.