Here are some pros and cons. This is admittedly from somebody who is biased since I buy, rebuild and sell Air Diaphragm pump systems. However, I also own and run a multi truck roof cleaning operation and use these things every single day.
Pros. Inexpensive to purchase. Simple to set up. Compact. Quiet.
Cons. High long term cost. Electric pumps are ultimately expensive to run because they burn out quickly and require frequency replacement in many operations. Including batteries. 4 Fatboys per year is what an air diaphragm pump and compressor run. Very limited in the types of nozzles you can use thus high materials usage. Needs a battery that you need to remember to charge.
Gas. (Udor/John Blue, etc.).
Pros. Relatively compact. Hits long distances due to higher running pressures. Higher output than electric. Somewhat more flexibility in nozzle selection than electric but limited to sensitivity of bypass.
Cons. Expensive. Reliability has been spotty at best. High pressure can be an issue if you get too close as you exceed the PSI limits of the roofing material. Has to run a bypass with high percentage chemicals. Requires refueling.
Pros. Most reliable of all pump systems if properly set up. Widest range of spray nozzles, lowest materials usage. Depending on pump and compressor, highest output and longest spray distance. Up to 50 GPM for a 1" pump setup (rinsing/materials transfer)). Fully rebuildable. Lowest overall operating cost of any pump due to rebuild ability, longevity and flexibility. Material savings. Available in materials which are completely immune to acids and high grade oxidizers such as PVDF/Kynar.
Cons. Most space intensive due to needing a compressor. Noise. Higher initial price vs electric. Cost of entry CAN be higher than gas with a large Air Pump setup (1"). More supporting equipment such as water separator required. Requires refueling.
Air pumps scare people because they don’t understand how they work and there are more pieces involved. This isn’t really a con as once they build the system and start to use it, they quickly realize that actual daily operation is simple…start the compressor and turn the air valve.
Last year, I sold over 50 AODD pumps, mostly used pumps that I rebuilt to save guys money. About 1/2 of them were to established cleaners and the other half were to newbies. The higher the percentage of SH you run such as for Tile roof, the better the AODD pump will look. Why nobody makes a Kynar/Teflon electric is beyond me. The majority of the established guys were electric pump users.