Actually quite the reverse, a larger diameter propeller will usually be more efficient, as the swept area is one of the major factors in propeller design. the power is transferred over a larger swept area reducing the load per blade area. a blade thats having to work hard will often come close to cavitating, which is one of the largest losses a propeller can have!I'm thinking a wider blade, reduced diameter prop is more efficient.
Another is the rotational momentum imparted to the water from the spinning 'disc', which is a function of the blade lift/drag coefficients and RPM. an ideal blade is one with a high Clift and a low Cdrag, but this is nigh on impossible! lift cannot be created without drag, so a highly loaded propeller will have a high Clift, but also a high Cdrag, which decreases rotational efficiency. you also have to turn a smaller propeller faster, which results in more rotational losses.
another way of thinking of it is this: A large merchant tanker will often have a very large propeller turning at less than 100 RPM. They will often design the stern frames of the vessel to accommodate the largest propeller possible! vessels like this are all about efficiency!
Source: Currently a masters student in marine engineering
ps. I know this is my first post, but I have been reading sailnet for some time and thought I could help!