According to wikipedia (and I have no idea if these critiques are correct)
Bourke engine - Wikipedia, the free encyclopedia
Seal friction from the seal between the air compressor chamber and the crankcase, against the connecting rod, will reduce the efficiency.[11]
Efficiency will be reduced due to pumping losses, as the air charge is compressed and expanded twice but energy is only extracted for power in one of the expansions per piston stroke.[12][13]
Engine weight is likely to be high because it will have to be very strongly built to cope with the high peak pressures seen as a result of the rapid high temperature combustion.[14]
Each piston pair is highly imbalanced as the two pistons move in the same direction at the same time, unlike in a boxer engine.[15] This will limit the speed range and hence the power of the engine, and increase its weight due to the strong construction necessary to react the high forces in the components.[16]
High speed two-stroke engines tend to be inefficient compared with four-strokes because some of the intake charge escapes unburnt with the exhaust.[17]
Use of excess air will reduce the torque available for a given engine size.[18]
Forcing the exhaust out rapidly through small ports will incur a further efficiency loss.[19]
Operating an internal combustion engine in detonation reduces efficiency due to heat lost from the combustion gases being scrubbed against the combustion chamber walls by the shock waves.[20]
Emissions - although some tests have shown low emissions in some circumstances, these were not necessarily at full power. As the scavenge ratio (i.e. engine torque) is increased more HC and CO will be emitted.[21]
Increased dwell time at TDC will allow more heat to be transferred to the cylinder walls, reducing the efficiency.[22]
When running in auto-ignition mode the timing of the start of the burn is controlled by the operating state of the engine, rather than directly as in a spark ignition or diesel engine. As such it may be possible to optimize it for one operating condition, but not for the wide range of torques and speeds that an engine typically sees. The result will be reduced efficiency and higher emissions.[23]
If the efficiency is high, then combustion temperatures must be high, as required by the Carnot cycle, and the air fuel mixture must be lean. High combustion temperatures and lean mixtures cause nitrogen dioxide to be formed.