I started using a Trangia a couple of years ago after four decades of Camping Gaz. Last year I took the meths version for a UK trip and a gas stove for a French trip. This year I've got a gas burner for the Trangia.
I thought there would be a clear winner, including the issue of weight, but there wasn't.
I would say that for the odd cup of coffee then a gas burner is cleaner, quicker and simpler. For everything else, the meths seemed cheaper and more robust. Incidentally I bought a 5 litre meths container to fill up from at home and that really is cheap!
One aspect (that may have been mentioned) is that IMV the Trangia has huge advantages over a small Camping Gaz stove in terms of windproofing and stability. This makes it look like meths is better, but of course it is the design of the stove. A gas Trangia is probably best of all but weight will creep up.
Which doesn't answer your question at all.