Mileage Question

Hello, I have a Question: As I understand it, driving a 2 x 4 generally gives you
better gas mileage compared to a 4 x 4. My F150 Lariat allows me to switch
between 2 x 4 and 4 x 4. Does using the 2 x 4 on my Lariat improve gas
mileage to the same degree as in a similar truck that only has 2 x 4?
As I am considering buying the new F150 diesel in 4 x 4  I was wondering if
this truck can switch to 2 x 4  on demand like my Lariat (which is how I would
drive most of the time) and if this would improve the mileage enough to
warrant buying the diesel.