What I've read so far:
CCD seems to be a quite sound approach and cost-effective solution, as it retains the standard diesel engines and uses normal diesel fuel, plus stored oxygen and an inert gas like argon. This would make a refit of existing conventional diesel submarines relatively easy. Thyssen Nordseewerke TNSW and RDM (for the Moray class submarine) offered solutions, which however found no takers. A drawback seems to be the higher noise level for high underwater speeds when the diesel has to take over.
Stirling is the oldest AIP technology (diesel fuel and liquid oxygen), with the least power output and the highest noise level.
MESMA uses a steam-turbine system, which burns ethanol and liquid oxygen to create the steam needed to drive a turbo-electric generator. It provides the highest power output of all AIP systems. The very high pressure-firing allows exhaust carbon dioxide to be expelled at any depth without an exhaust compressor, and very deep diving depths of up to 600m can be achieved. However, the efficiency grade is quite low, and therefore the oxygen consumption is correspondingly higher. Quieter than the diesel powered AIPs, but noisier than fuel cell AIPs.
Fuel cell technology is offered by HDW and Siemens in Germany (U212/U214) and uses hydrogen and liquid oxygen and seems to be the most advanced and quietest technology currently available. The problems are the inherent danger of using hydrogen, therefore storing it in several metal hydride tanks, and the cost to produce it.
The Canadian Ballard fuel cell technology uses methanol which can be stored in a single tank. The necessary hydrogen is extracted from the methanol using a so-called 'reformer'. The advantage is that ethanol is a renewable resource and that it apparently holds 40 percent more hydrogen atoms than a similar volume of metal hydride. The disadvantage is the added complexity of the 'reformer' and a compressor for carbon dioxide exhaust disposal, otherwise limiting the diving depth of the submarine.