The F150's last generation had 3.7L V6 non-turbo, 3.5L V6 twin turbo, and a 5.0L V8. The Raptor also got a hyped up version of the 6.2L V8, but we'll leave that truck out of the discussion as it has over $3000 worth of shock absorbers, so I really do not think fuel economy was high on the list of attributes for those buyers.
Since there is such a giant span of curb weights with F150s, it is tough to lay a good rule of thumb to ALL of them with ALL the engines. A regular cab long bed 2WD truck is going to weigh less than a crew cab 4WD truck, even if that crew cab has that stunted useless 5ft bed on it. They also have different tire and wheel options, rear axle ratio options, etc. They call get the same 6sp slushbox.
The current generation went on a major weight savings plan with the aluminum body, so all versions are lighter. They also replaced the 3.7L with a non-turbo 3.5L, as well as added the 2.7L "Nano" V6. The 3.5L turbo and 5.0L V8 are carryover, with a couple of minor tweaks.
Driven with little to no load, the V6s (all of them) are going to use less fuel than the V8. The difference comes when they are loaded, then obviously the turbo engines will suffer more, because they have more available power to be made. I think the 3.5L turbo can do everything the 5.0L V8 can, but how much fuel it uses is largely dependent on how much load you are asking of it. Personally if you are driving around with a heavy load most of the time, a 1/2 ton truck is probably not the best choice anyway.
The Nano V6 seems pretty frugal, that is what my Dad bought. It is peppy to drive unloaded, and has good punch to get up to speed when you need it. It is surprisingly quick for its size. It can get into the mid 20s MPGs with light load and moderate speeds. His is a supercab, short bed, 4WD. Their previous F150, a 1994 model with the same cab configuration only 2WD and it had the optional 4sp slushbox would get about 19 asking it to do the same task. And it wasn't nearly as peppy (not even close). However, I doubt this new truck will give them the 300k miles of very low cost of service that the '94 did. Seriously, the 4.9L I6 in that truck never needed anything but oil changes and ignition parts changes, a thermostat, and I think a TPS once. That is about it. Didn't leak oil, didn't burn oil, didn't do anything bad. Big low tech lump of iron.