The latest generation of high bypass turbofans have really blurred the distinctions between turbofans and turbo props. Both in noise and fuel burn they have gotten rather close - to the point where other factors come into play as to which is better.
Propulsion theory says that you get the maximum efficiency when you accelerate an infinite mass of air an infinitesimal amount. Obviously, an infinitely large fan (or prop) isn't practical, but that's why you see ever increasing bypass ratios on the current generation of turbofans w - most have a bypass ratio around 10-12 (by contrast the early JT9D was around 4).
To a first approximation, propellers are a constant power device, while pure jets are close to a constant thrust device. Since thrust equals power/speed, that means that props are most efficient at low speed, while jets are better at high speed. Hence props have very good takeoff performance and the early pure jets struggled to get off the ground, but happily cruised over Mach 0.8. Turbofans sort of split the difference - they lose efficiency as they go faster, but are still better than pure jets (at least subsonic).
Two things that hurt props compared to fans is that fan duct. Props don't need to carry the weight of a fan duct, but fans have exit guide vanes that take out most of the swirl (improved efficiency), and that duct provides acoustic treatment to lessen the noise footprint. Counter-rotating props can improve the efficiency by taking out most of the swirl, but they create tremendous noise.
Unlike Less Hair, I don't think unducted fans are the future. Noise is a major issue, as is a blade release since there is no containment. I know people who worked the unducted fan 7J7 project - apparently the noise from those counter-rotating props was deafening. As for a blade release - I spent some time working a turboprop project, using the same Allison engine/prop as the C-130J. A prop blade release was considered catastrophic - not because the blade might go through the fuselage, but because the resultant out-of-balance vibration would structurally fail the wing.
