how much more efficient are rotary engines than conventional engines?

Answer 1

Rotary engines are less efficient than piston engines.

See:http://auto.howstuffworks.com/rotary-engine5.htm


There are some challenges in designing a rotary engine:

Typically, it is more difficult (but not impossible) to make a rotary engine meet U.S. emissions regulations.

The manufacturing costs can be higher, mostly because the number of these engines produced is not as high as the number of piston engines.

They typically consume more fuel than a piston engine because the thermodynamic efficiency of the engine is reduced by the long combustion-chamber shape and low compression ratio.

Answer 2

Also the internal parts require a much higher level of machining. Most standard piston engines can get by with .001 tolerances (or less).
Apex seals commonly go bad within 60-70 thousand miles also. With the future improvements in materials, the rotary may pass conventional engines in the future..but not yet.