siemens PEM fuel cells: (Fuel efficiency 60%.) They use compressed hydrogen and oxygen (may be liquid) to run the fuelcells. US navy uses this in nuclear boats too. There the added advantage is under submerged condition they can reverse the fuel cell operation and electrolyze water to oxygen for breathing. Except for getting food for sailors the boat has no need to come out of water for 20 years.
(I applied for a job to do this research work at Siemens when they received the contract from US navy around 2006~08. my application was rejected for not being an USsie. Now I am in India not contributing anyway to further fuel cells research
Li-ion Batteries (LIB): Hi power density, no moving parts, no gas emission and relatively high turn over el. efficiency (80%). Though energy density is relatively poor so for the given volume space in submarines LIBs are suitable only for 2 weeks. Beyond that one need fuel driven preferably diesel or H2 for fuel cells. I am sure Japs arrived at this time frame after doing optimization studies. Only compressed gas is Oxygen for breathing. no Hydrogen, no fuel tanks.
So this will be the quietest, but little bit expensive AIP. Only Japs know how to make LIB economically.
In cars their role is limited because of the cost increase does not match the performance gain over the Ni-MH batteries. So Toyato, Nissan etc switched over to Ni-MH batteries. Boeing accident was due to charging circuits.
Conventional PAFC: Dis adv: Low power density. It needs 10 times the size of PEMFC to give same power. Fuel efficiency 40% at the biggest optimum size. needs high Platinum loading. Phosphoric acid vapors coming out of the exits will corrode metals if not treated properly. Op. Temp 180~200oC. (search for UTC fuel cells. I dont know the name of the new owner)
Adv: can run for 65000+ hours.
Modern membrane PAFC:Op temp 120oC. power density increases But the durability is significantly reduced to 500 hours. plus all the above relevant disadvantages.
The main advantage of PAFC is they can run on diesel (DRDO might have chosen PAFC for this reason) by adding accessories which convert diesel to hydrogen and Carbon monoxide (CO) on board. CO acts as fuel at temp above 200oC. But these accessories will significantly increase the volume and hence not suitable for submarines.
Agility in drawing power LAB > LIB> PEMFC > PAFC.