I'd try and be more specific towards the kind of the fuel we are talking about:

 1. White Gas

   - Burns clean without any smell and/or effect on food taste.
   - Accidental Spilling of the fuel is not much to be worried about. Evaporates very quickly, without leaving an odor. That said, make a note that the spilled fuel is very flammable
   - White gas is safer to store and transport than probably most of the other products.
   - Additional information: White gas is basically gasoline without the additives you find in the stuff that goes in your car. (Credits: A comment from Mark, below)

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 2. Propane Gas

   - A Propane gas stove would most likely be a Canister type? So, pressurized fuel? : Might be more dangerous if canister is leaking?
   - Most of the products that are available are the ones that work on Propane and Primarily Isobutane. They burn hot and clean.
   - Pressurized fuel = No Pumping, preheating required.
   - No spill play at all as the canister holds the pressurized gas, so self-seals when the stove is detached: Safe!
   - As you don't pour the fuel into the canister, its difficult to gauge remaining fuel level.
   - Performance degrades as the fuel is consumed since the pressure is released. So, when *nearly* emptied, the remaining fuel is apparently useless.  
   - Fuel is more expensive. 


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 3. Kerosene Stove

   - function really well in extremely cold temperatures.
   - Burns hot, better than Alcohol stoves.
   - Relatively inexpensive fuel.
   - Needs proper storing, since it evaporates slowly if spilled.
   - Prone to spills during the pouring process. But, spilled fuel won't ignite easily.
   - Not Odorless.
   - Many of the Kerosene based stoves need pumping and pre-heating.


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Some points about common terms used in different parts of the world. Thanks to [A E][1] for suggesting this concept and the data provided. I have done a mere copy+paste from comments.

It would be helpful if this question/answer also contains the translation for non-American readers.

 - In the UK, *'Coleman fuel'* is same as what is known as *'White Gas'* in America.
 - Terms for *'Propane'* and *'Butane'* are (somewhat) universal.
 - US *'Kerosene'* is UK *'paraffin'*, the same in India is *'Kerosene'* and more popularly known as *'Rockel'*.
 - US *'Gasoline'* is UK *'Petrol'*.
 - In the UK, they also have *'White spirit'* which should not be confused with *'White gas'*, it's not the same thing.
 - *'White Gas/Coleman Fuel'* is called *'Naptha'* in Eastern Canada.


  [1]: https://outdoors.stackexchange.com/users/4098/a-e