I have been using catalytic (Olympian Wave series) heaters in my campers since the ’90s. These heaters are designed for indoor use with the caveat they must be vented because catalytic heaters deplete O2, which increases the percentage of CO in the air, as several folks have already mentioned. These heaters require at least 24 square inches of open air venting. No batteries.
Some catalytic heaters come with an oxygen depletion sensor that shuts off the heater when O2 gets low. Problem is they often shut off the heater at higher altitudes due the smaller content of O2 in the air — not the depletion caused by the heater — so they just don’t work at altitude.
Propane is heavy with the required thick tank (or canisters). You can buy a 11 lb. (2.5 gallon) propane tank that weighs 14 lb. empty and 25 lb. full. One problem is most propane sellers charge a minimum fill up price equal to 5 lb. of propane. Batteries are heavy too. I have a 100AH LiFePo4 lithium battery for my telescope kits. It weighs almost 25 lb.
Catalytic heaters create radiant heat, which doesn’t work well in a tent. Back in 2003 I did some experimenting with my small tent trailer (can’t find the data). I cut out panels of reflectix insulation to cover the tent material and this made a huge, significant improvement in room temperature. I also did some experimenting with some non-insulated reflective material, which did make some improvement, but not nearly as much as the reflectix.
I’ve never had condensation problems, but usually camp in deserts when using these heaters. We have camped when it rained for several day without condensation. I suspect the open air space requirement helps mitigate condensation.
Here’s a long-term review of the Olympian Wave 8 heater from my website. There is also a link to the Owner’s Manual in my review.
I would not consider a catalytic heater for backpacking or any kind of heater that required fossil fuel or a battery. Insulation (worn or sleeping bag) would be my solution. I have never used a wood stove designed for tents, but if I did, I would want a firebox large enough to minimize the amount of time spent feeding wood into it. Unfortunately such a large stove might not be practical weight-wise for backpacking.