To answer your second question first:
Generally, it is always better to accelerate a big amount of air a little than a small amount a lot. Therefore, the helicopter rotor is much more efficient when creating lift, similar to a propeller which is more efficient than a jet. In the same way, more wing span reduces induced drag since more air can be used for lift creation.
The advantages of a lift fan are mainly due to its compact size:
- Low mass, low inertias
- Compact size, therefore easy to tuck away for fast flight
- Low torque for a given amount of lift
and the disavantages stem from the same source:
- Low efficiency
- High exit speed, so beware of the blast.
- No autorotation possible when the engine fails.
- Lift acts at the center of the fan, so you need additional jets for pitch and roll control. A helicopter can shift the center of lift away from the rotor axis (within limits) by using cyclic changes to the angle of attack of the single rotor blades.