Not an easy question, and it is not only a matter of power density or efficiency in general. Several constraints apply (i.e. regulations on emissions), and talking about power density or efficiency or even specific consumption, without an adequate reference to a reference duty cycle, is meaningless, or just good for catalogues and brochures. Dual-fuel I.C. engines show a relevant potential, due to the adaptability of the control strategy applicable (modulation of the power/torque curve). Also integrated strategies aimed at keeping the ICE point close to its optimal point will play a role, as well as powertrain architectures, regeneration and hybrid systems, both on- and off-road. Each application can take advantage of multiple solutions, and the best TTW or WTW efficiency depends on application. In the future we will see more and more specialized solutions applying different strategies.

LPG is composed of propane and butane but natural gas is composed of the lighter methane and ethane, so LPG has a higher calorific value  (26.1kWh/m3) than natural gas (10.6 kWh/m3)... It is important to make an engine on a gas consumption basis, if so, I think LPG could be better than NG(compressed) duo to its lubricity characteristics, how ever experiments indicate that after a period of 2-4 years, damages would happen to the engine compared to the same period for Diesel or Petrol engines.

After all, I think it's more efficient to spend time and money improving petrol and diesel engines, considering the efficiency and emissions rather than working on NG engines. 

In comparison between gaseous fuel, liquid fuels like gasoline/diesel have higher heating values (LHV) but are not environmental friendly fuels.  Since their emission can be solved by using catalytic converter (SI engines), particulate traps (Diesel engines), and advance techniques.  However, the followings shall be considered; high fuel conversion efficiency, safely operation and handling, environmental impacts, and importantly, supply/demand which directly affects fuel prices.  Alternative fuels like biofuels are potential fuels for vehicles which pros and cons shall be seriously discussed and further developed.  For example, ethanol having high ON, having comparatively high fuel conversion efficiency but having problem with aldehyde from its combustion is for gasoline engines and biodiesel having higher lubricity and high fuel conversion efficiency but higher viscosity is for diesel engines.  It is not so secure to rely and depend on petroleum fuels - easily to pump out to serve people around the world but takes million years to form.

First point: when comparing different fuel DO NOT use specific fuel consumption but energy specific consumption or just energy efficiency. 

About power density. If you are talking about an atmospheric engine, OK, natural gas engines have less torque or power, although LPG liquid injection engines can actually have higher torque and power than petrol engines. But if you use turbo-charging, there is no reason why natural gas engines should have less torque or power than petrol engines.

In fact gaseous fuels (hydrogen and natural gas) have a huge problem because of their energy volumetric density (not mass density), but this is not entirely correct with LPG and DME because they are liquid at the pressure for injection. This is the reason I do not believe in the "hydrogen economy", who is it possible to choose the WORST fuel?

But nobody discussed DME. For me it is the WONDER fuel, used in diesel engines (very efficient engines) and with the benefice of promoting a perfect mixture preparation. 

In general, petroleum fuels are much better than natural gas in terms of performance. Weight to power ratio and brake specific fuel consumption of gas engines are more around 30 and 200, whereas for petroleum fuels around 2 and 300. Speed in rev/min for gas engines is also very less when compared to petroleum liquid fuels. Petroleum fuels can be easily stored whereas natural gas faces difficulty in terms of storage and design to store.