Both fuels have roughly the same specific fuel energy/weight ratio.
Ethanol fuel such as bio ethanol does better than methanol.
There are also gels fuels, which are gelled Methanol. These are somewhat safer to use than liquid fuels.

Evernew does a nice Trangia replacement but it is not as efficient due to its higher faster burn times. Trangia fuel bottle work well.

Esbit is messy, but can make for very lightweight stove kits

All the fuels above such as alcohols, gels and Hexamine fuels can be problematic is very poor weather conditions.

Why not stick with a good quality stove burner like the Soto Windmaster and some good quality fuel for cold weather using a isobutane/propane mix from Jetboil.

For really cold weather my stove fuel combo might even be a

Coleman Propangas cartridge
Kovea LPG Adaptor
Firemaple Stove