We have the 2012 Silverado 1500 5.3 6 spd 3:42 towing a trailer 31 ft overall weighing 6500 lb when travelling (5400 lb dry). The truck handles the trailer very well. So far we have traveled Ont to the east coast, Ont to Florida and now Ont to New Orleans to Tucson Az.
I always use tow haul ( and turn on headlights) when towing. I let the transmission choose the gear. When in tow haul the engine braking feature does work - the transmission shifts down to a lower gear to hold the speed on steep downhills.
We get about 10 MPG / US gallon when towing.
The 2014 has some more power than my 2012.
I hope my experience helps.