I have a tune on my truck and it did improve fuel mileage (towing and not) and towing power and no nasty side effects.
If you do start messing with the tune get at a minimum an exhaust gas temperture gauge (EGT) because you can get into trouble if you do not watch it. Also keep in mind as in the case with the early Alison trans 5 spds, you can produce more power than the transmission was designed to handle in stock form. Not so much an issue with later years.
Lastly, once youhave a tune do not rely on fuel mileage data from the Driver Information Center (DIC). The non-stock pulse rates mess with the calculations. My truck is off 3 MPG from DIC to hand calculated.
JIm