I have a 3-way reefer in my coach (Propane, 12VDC, 120VAC); I run it on 12V on the road. I installed it a couple of years ago, and it was $1,200 and only 7.5 cu. ft. I ran my old 2-way (Propane, 120VAC) on an inverter underway. As noted, one gets more space and features with a residential. One of my good friends owns a large RV repair shop and he will not install an evaporative reefer. As a footnote, a friend has an all-electric RV reefer.
As far as the tow vehicle's being able to keep the reefer battery up, note that modern residential reefers use little power, and because they're better insulated, the compressor only has to run intermittently. While there may be a net drain while the compressor runs, it's a very short duty cycle, and the battery can catch up.
Many RVs run the reefer on propane while underway, but like arveetek noted, it should be avoided. A friend of mine blew a tire, and the steel cords took out his propane line; thankfully he noticed the leak right away and shut off the gas. Fortunately, he was in transit near my house, so I brought the flaring tools and tubing he needed to repair. My old motorhome had a 2-way, and I had a note on the dash to shut the reefer off when refuelling.
Another footnote, I replaced the 12V house batteries with 6V golf cart batteries in series - more capacity, and hardier.
'94 Barth 28' Breakaway M/H ("StaRV II") diesel pusher: Spartan chassis, aluminum birdcage construction. Peninsular/AMG 6.5L TD (230HP), 18:1, Phazer, non-wastgated turbo, hi-pop injectors, 4L80E (Sun Coast TC & rebuild, M-H Pan), Dana 80 (M-H Cover), Fluidampr, EGT, trans temp, boost gage. Honda EV-4010 gaso genset, furnace, roof air, stove, microwave/convection, 2-dr. 3-way reefer. KVH R5SL Satellite. Cruises 2, sleeps 4, carries 6, and parties 8 (parties 12 - tested).
Stand-ins are an '02 Cadillac Escalade AWD 6.0L and an '06 Toyota Sienna Limited.