I've logged every tank of gas on 3 trucks: 2 of those 3 have only ever had dino oil - Delo 400 15w40 in the diesel, and 10-30/40wt in the 22RE.
The 3rd one, a 3.2L V6, I've experimented with a variety of the Havoline oils -
5w & 10w30 Havoline
10w-40 Havoline
10w-30 Havoline HM
5w-40 Havoline synthetic
5w30 Havoline Blend
And I've even ran a few rounds of Rotella synthetic diesel 5w-40 oil
I have only, at most, noted a 1-2mpg increase/decrease - but in the increases came with highway driving, no wind, no load; decreases came from opposing conditions, i.e. heavy wind, top-heavy load, etc.
Overall, I feel the engine has been the quietest with the Havoline blend; but had the best overall power with the Rotella synthetic.
All in all, the mileage difference is not enough for me to say that synthetic is better for miles per gallon.