I tried heating 3 gallons of tap water in a 5 gallon pot on the side burner of my Weber grill, the pot was slightly too large for the burner. It works if you have a pot that fits, but it takes a long time to boil. This was ok for my purposes as I was just heating the water in case I needed to top off the boil kettle or I needed some sterile water for some reason. Otherwise, I wouldn't use it brew on. I like a vigorous boil for brewing and this burner just didn't get hot enough to give me a good rolling boil.
I've used my side-burner frequently with no issue. I wouldn't use the grill plates though. Not sure how much more or less efficient it is overall, but my wife prefers when I do this because I don't "stink up the house"
+1 to pleasant aroma
Even my non-beer drinking friends can tell and comment on how my place smells like a bakery after I'm done brewing. That said I do try to brew outside as often as possible to keep moisture levels down.
I don't understand the "stink up the house" complaint that some SWMBO'S talk about. Mashing grain has no smell and boiling wort smell "grainy" sort of like bread. Lucky my lady doesn't complain and besides I do it outside. But before I got the gas burner I did it inside w/a 15oo watt electric plate.