I have the 6,000/ 12,000. I believe that's the size and it works well but the fumes are the issue. We may be more susceptible than others but we notice our sinus start to get plugged and we can just tell that it's in the air.
Then there is the issue of temperature variation. As we get older we like it to be one consistent temperature and that cant happen without a thermostat.
You mentioned the wave heater and I have asked a few people about it as I have considered it. I believe it's a notch up from the buddy and is possibly cleaner burning and more efficient.
The next step up is the Cat Platinum which is vented to the outside. It's not as 12 volt hungry as a house furnace but does use a couple amps for a few minutes during ignition and then drops to about .5 amps to power the exhaust blower. It uses through wall or roof 1 1/2 inch pvc for its exhaust pipe so it's probably pretty energy efficient.
I think the Buddy is a great value if it works for you. I dont think the wave would be bad at $300.00 or so and I would bet that the Cat Platinum is the top of the line. Their methods of combustion aren't all the same.