First off, no, using propane (or propane accessories, as Hank Hill would say) in the garden is NOT green. Greenhouse gas is more like it.
Um, they are only moderately effective. Good for frying emerging seedling weeds. Not all that effective on deep rooted perennial weeds like dandelions, quack grass, dock, etc. You can cook the tops to the point they are black char, and the insulating effect of the soil will protect the root below, and in a week or two, the weed pops back up. And, it actually takes longer than you would think to kill a weed, most you have to hold the flame on for 30 seconds to a minute, except for the most tiny flimsy baby weeds. So, it's kind of a slow process.
The thing I've found it best for is to cook the weeds that grow between the expansion joints in my concrete driveways and sidewalks. I can hold it over the weed long enough (1 to 2 minutes) to generally kill the roots in the limited soil volume that accumulates in the expansion joint. At least it beats pulling them by hand.