I routinely do 10 gallon batches. I use the SP10 Bayou Classic High Pressure Propane burner (185,000 BTUs max). http://www.bayouclassicdepot.com/sp10_propane_burner.htm
It is noisy when it is on full-blast, but it will heat 17 gallon of water in a 20 gallon SS kettle to 150+ F in about 30 minutes.
After the first runnings are placed in the boil kettle, I start the burner, and take it above Mash Out temps while lautering (typically batch sparge method). Depending on the intended style (e.g., if I want a light colored beer with no kettle mailliard reactions), I may stir the high-gravity first runnings frequently, and keep the burner turned down lower for the lighter beers, and on full-blast for the darker beer styles that accept kettle-derived Mailliard reactions.
I collect the wort in a 5.5 gallon SS kettle and dump it into the 20 gallon SS kettle. Lautering takes about an hour. During this whole time, the ever increasing volume of wort in the boil kettle is being heated and never quite makes it to a boil by the time I transfer in more wort. By the time I'm done lautering, the wort is practically at boil temps and we're ready to deal with the hot break and start the hop additions. IMO, I don't think you need a bigger burner. I am intrigued, though, by the banjo burners that are supposed to be quieter.