I recently spent some time sorting out the terminology and various parts of propane burners because I was upgrading mine.. I am no expert but based on what I found:
Cookers are basically made up of a stand, a burner and a regulator. The max btu output is primarily a function of the regulator and the size of the small hole drilled through the center of the orifice fitting at the burner end of the hose. Those control the max rate at which the propane is delivered to the burner - more propane = more heat.
The actual burner, such as BG12 or BG14 (or BG10) seems to affect how wide the flame is distributed - the flame diameter for these burners. This seems to have little affect on max heat output. Typically, you want a burner face diameter somewhat smaller than your pot. Flames lapping up the side of the pot waste heat / propane and may damage equipment attached to the pot.
Banjo type burners like the BG 12 and 14 may be better at maintaining a low flame.
High vs low pressure is a function of the regulator, not the burner. "High" pressure means anything above about 1 psi, and is intended for outdoor use only. "Low" pressure is in the one-half psi range. High pressure regulators deliver more propane, so have higher max heat output.
Other things to think about are how well you can adjust the flame to get an efficient burn and how well it can maintain a low flame when turned down to maintain a boil after the water / wort is heated.