I did quite alot of looking into gears before I bought my bike, paying particular attention to whether a double or triple would be better for me. At first glance a triple is better as it should give a lower ratio. In reality however it depends on the size of the rings you are using. All doubles are not the same, nor are all triples nor all cassettes. You can get complicated and work out crank lengths and srtoke lengths, or as a more general rule of thumb, simply divide the teeth on the front ring by the teeth on the cassette to get a ratio. Do this for a range of bikes and you can compare the standard set-up on each.
I did this for a range of bikes when looking for mine, and was surprised to see that some doubles (such as the Boardman bikes) were lower geared than some leisure/commuter bikes with triples. Again, as a general rule of thumb the more road-bike a bike is, the higher it will be geared - for speed. The more a bike tends towards off road or mountain bike the lower it will be geared. Again as stated above, there is also redundancy within gears such that the same ratio may be available on several front and rear combinations, and the distance between successive gear changes may be smaller in terms of ratio the more gears you have.
Pro or competitive cyclists will tend to change gear rings with the terrain they are riding, for us mortals you pays your money and takes your choice. A triple doesn't necessarily give you a wider range, but it is likely to give you smaller steps between changes and more redundancy. Having a triple is a useful fallback even if you only use it once in a blue moon, which seem to happen quite often round my way.....
Steve.