There are a few distinct differences between a propane and butane cooker.
They are both popular, and you will see a lot of them around.
Butane tends to burn more efficiently than propane, and it's also cheaper to purchase.
At the same time, you usually only buy it in small canisters which run out quickly, they don't like to be bumped around (or shaken when you are walking etc) and they will freeze up in temperatures below zero.
This is a serious issue if it's the source of your warmth in the freezing cold! I much prefer Propane because you can get it in bigger bottles, it won't freeze as easily and you can throw the bottles around all day and it won't affect the way that the cooker runs.
At the end of the day though it comes down to what you want.
I have seen a number of people buy butane burners which are only around 20 dollars, and then you just use the cans of butane in them.
The only issue with these is that they tend to burn quickly; a single can might last you for a few meals, but that's not always the case.
The end result is that you end up with a lot of litter and they take up quite a bit of space.
However, they are cheap to run and they start automatically (with a click of a button).
I would suggest that if you go camping regularly then having a propane burner is a better option.
Of course, consider your weight and size restrictions too!