It will pull somewhat easier. You're trading low end torque for high end speed. Depending on a lot of variables, you'll see some improvement when starting from a roll and accelerating (and fuel economy to go along with it). You'll also see some (again, depending on a lot of variables) loss of fuel economy when you aren't towing...probably not noticeable in city driving and more pronounced at highway speeds. Honestly, if you're only pushing around 3500 rpm when climbing, I'd just continue to downshift and roll with it. It doesn't sound like it's really struggling and you'll likely only get about 2 mpg or so by swapping (while towing). Consider how long it would take for that to pay for itself based on how much you pull with it. Will it improve your towing?...probably. Is it worth it?....depends on your situation. If you have 4WD, double the price.
2012 Chevy Tahoe LTZ - HD tow package
2017 Rockwood 2703WS Emerald Edition