I have some experience with using mecanum wheels, both indoors and outdoors (on grass, sand and dirt no less).
Obvious advantage is holonomic movement. Disadvantages are weight (commercially available wheels are ridiculously heavy) and cost. For a given tread material traction will be along the lines of 65-70% that of a regular wheel due to the smaller contact area and 45% rollers.
Compared to skid steer, mecanum wheels have no additional friction when turning which is an advantage.
Mecanum wheels will be simpler and perhaps more reliable than a swerve/crab drive system.
Everything is always about tradeoffs. If I compared an ideal mecanum system to an ideal swerve drive system (full 360 degree rotation, extremely fast wheel orientation) the swerve wins in performance because it has full traction.
An ideal swerve system will be expensive and difficult to implement compared to mecanum wheels though.
Efficiency is a loaded question. An ideal mecannum wheel will be equivalent to any other system when moving in any direction, and will turn better than a skid steer system.
In reality the rollers have reasonable friction so going sideways will be less efficient than going forwards.
Getting exact numbers would require a lot of fairly accurate measurements which isn't practical.