Yes, combustion gas is hotter with LPG
LPG produces less power (unless injected as a liquid), and uses more litres per 100kmthan gasoline/petrol, so you lose overall range between refueling.
You also lose cargo space of you put a tank inside, of lose ground clearance of you put tanks underneath.
Many Australian vehicles are/where converted to run on LPG because LPG was heavily subsidised by the Federal government making it very cheap.
Lots of vehicles burn exhaust valves, and wear valve stems and seals faster because seals are no longer lubricated with liquid petroleum from the air/fuel mix.
Many vehicles get fitted with a drip feed lubrication system to lubricate valve stems.
I've weighed the cost of installation, certification etc of LPG in the past, and with subsidies on fuel costs, it was still a 7-10 year payoff based on fuel savings on moderate mileage (15-20k/km per year).
In Australia, LPG tanks need to be pressure tested and re-certified every 10 years. This along with maintenance of the system generally means that your 10 year pay back just evaporated.
Evaporator systems don't like cold weather. Many vehicles need to be started running on petrol, them switched to LPG.
In Australia, LPG can be hard to find in smaller towns. In cities, you'll find your regular refilll spots.
Personally, anytime I'm looking for another vehicle, a vehicle that has an LPG system is given a hard pass. Even if everything else was perfect, I'm scratching that vehicle off the list.