Since we last discussed it, I saw something in one of the tankless models that turned me off - in freezing weather, it has to fire up every so often to prevent itself from freezing. It makes sense; it just wasn't something I thought of before, and many people don't camp in freezing weather, so they probably wouldn't notice.
Since we do regularly camp in freezing weather, and we don't want to listen to it cycling on and off two or three times an hour while we're trying to sleep, we've decided a regular tank model is the best solution for us when it comes time to replace ours. We can heat the tank of water before we go to bed, then shut it off, and it still won't freeze by morning. Also, it'll be quiet and use zero propane until we fire it up in the morning before our showers. The anti-freeze cycling might even offset any savings in propane we would expect; of course since we turn ours off when we're not using it, we probably wouldn't save much propane with a tankless anyway.
I'm really glad I saw one in operation in freezing weather before we took the plunge - I would've been extremely disappointed. I still think they're interesting technology, but they're just not the best solution for our usage patterns.
1995 Airstream Classic 30' Excella 1000
2014 Ram 2500 Crew Cab with Cummins 6.7L Diesel
Sold but not forgotten: 1991 Airstream B190
Sold: 2006 F-250 6.0L Powerstroke Supercab