I've used a jetboil flash, and I've used a trangia spirit burner. I'll try to be concise with my needs and experience.>using jetboil flash
I like coffee while I camp. I use the fogler's coffee bags, very nice. The jetboil flash was pretty good for this, just boil your water, pour into mug, wait. The coffee, when done steeping, sometimes cooled to the point of iced coffee in the winter though. I really like ramen when I'm out, sue me. Jetboil flash was not so good for this. I have to either break the noodle puck up and cook in the flash pot, or boil water, place noodle puck in my 775ml pot, then pour water over the noodles. Not a bad solution but again in winter, you get warm soup,not hot. Can be remedied by just putting the pot on the fire though, which I started doing. Cooking mountain house meals is a breeze with the jetboil flash as well, the pour spout comes in handy. The fuel is a little on the heavy side, kinda of bulky for my taste, and about 6 USD a piece IIRC. >Trangia spirit burner
I like this one just a bit more, just to preface. The unit itself is very small, the fuel is as cheap as a bottle of isopropyl alcohol can be, and you can use it in any weather. I pair mine with a little cross piece so I can set mugs or pots on top of the flame. I don't use a wind screen, it's usually enough to just make a divot in the dirt and place the burner in there. I like the burner especially for coffee since I can boil and steep water at the same time, same with ramen. The advantages in my eyes are>small>cheap>versatile>bulletproof
Disadvantages are really (imo) just>takes about 10-15 minutes to boil water
I will end by saying the jetboil is an ingenious product, I like it, and most of my issues with the jetboil flash are solved with the jetboil minimo. I also had to modify my trangia setup slightly, essentially just adding a spout to my 775ml cook pot. All of my trangia gear fits perfectly in my pot,including food.