There are many factors which will influence your decision. Obviously budget is a big consideration. Typically a decking will cost more than a patio. Simply due to the fact that timber is generally more expensive than flags. However this balance can change depending on the size, shape and material that you would like your patio made from.
There a advantages and disadvantages to both decking and patios. Some of the advantages of decking are:
Works well on uneven terrain
Decking can be installed on any type of land and is levelled on the supports.
Good for a view
Since a decking can be built up to a height with steps it can provide a better view.
Wooden decking can be stained or painted any colour so you can even match it into the decor of your house if you wish.
The disadvantages associated with decking are:
Depending on the material used and where the decking is situated it may need cleaning and sealing/painting every few years.
Wood is more susceptible to weather and can rot over time although, if treated correctly and installed well then it should last for many years to come.
While the price depends on the material and size, decks are usually more expensive than a patio of similar dimensions.