http://sheldonbrown.com/gears/
Put your front chain ring and rear sprocket sizes in the above calculator and compare to your heart's content.
I have 8 spd Campag rear hub with sprockets 12-21 on my hybrid and recently purchased a new 13-26 set of 8 spd sprockets as I couldn't find individual 23T and 25T sprockets. I intend slipping on the 26 sprocket when I do touring in the Alps or Devil's staircase in Wales should I feel the need. But 12-21 is currently fine for me in flatish terrain. I have a triple chainset 53-42-30 up front as sometimes the load I carry can be heavy but very seldom use the 30T chain ring unless I drop down to it by mistake.
However on my road bike I ride with a Shimano Ultegra 53/39 double chain set with a 9 spd Ultegra 12-25 rear cassette. These is no hill I have not been able to get up
.
So TBH I would have thought there would only be marginal gains going from 12-25 to 13-26 rear sprockets in climbing terms but you may also have different intervals between other sprockets and you will spin out at a slightly lower top speed having the 13 as your lowest ring. The Sheldon Brown calculator can also show your speeds in each combination of ring and sprocket.