I have both here – a couple of Esbits (which are cheap enough for everyone to have one..), and a Trangia metho' stove..
The Esbit is probably better for shorter and quicker trips; but I would prefer to take the Trangia for longer trips (though the Esbit could be small and light enough to take anywhere as a 'backup'..). The alcohol stove would be quicker to cook with, and cheaper to fuel over a few days – making up for any inconvenience from extra weight, or time setting up.
[ I also have an MSR multi-fuel stove, as well, which could be better for higher altitudes, colder temperatures, or international travel – but that's not part of this discussion..].


