I guess the most important factor is how much energy is lost in synthesizing/burning it. Do you have those numbers available?
I know methane can be synthesised, but it requires you to first make hydrogen, and then you'll lose an additional 50-60% energy in turning hydrogen into methane.
For any large scale operation I can't imagine that kind of energy loss is acceptable, hydrogen storage is difficult, but not THAT difficult
For ships and planes, we may be able to use lower carbon synthetic fuels like ammonia or methanol, and not have to go as far for synthetic fuels.
Pulling carbon dioxide directly out of the atmosphere is really inefficient. There may be cheaper ways to sequester carbon but they won't give you CO2 for making fuels. Hydrogen is definitely more efficient.
I'm not aware of any way to create synthetic propane using renewable energy sources, but that might be my ignorance speaking. A quick googling indicates it's not possible, but I'm happy to be proven wrong here if you want to provide a reference I didn't find.
Easier and cheaper doesn't really cut it for the climate. Petroleum is easy and cheap, and so is coal. Both are terrible ideas in the long run though
Liquid fuel is so energy dense that if you have to synthesize it and remove an equivalent amount of carbon from the atmosphere it’s probably still easier and cheaper than hydrogen.