Efficient cooling system for a DNA Analysis thermal cycler
Its not about efficiency, its about choice of application. If I am making an air conditioner of 1000 watts, I will still choose conventional vapor compression ( even though it has thousand times more global warming potential than carbon dioxide itself, and high efficiency thermoelectric materials ZT > 2, are still in development).

But for smaller loads 10 watts, 20 watts, 100 watts etc. ,to actually cool them, or cooling/heating/thermal cycling, thermoelectric systems are better, nor will I get a 20 watts air conditioner in market. 
The best part about thermoelectric systems is the response time from heating temperature to cooling temperature and vice versa, its very quick in seconds especially in your case, where cooling load is generally small in PCR.

Now, I do not know the response time and what is required in your test, but you should check that whether your above proposed systems will respond quickly to required temperature in the desired time, as you want them.

You can make thermoelectric cooling heating system yourself, its quite simple.