Sets of strings are gauged so that with standard guitar tuning they feel nearly equal in tension. String tension is obviously related to scale length and pitch but for any given guitar it is not the string gauge itself which is important but the mass of the string.
Of course as the gauge increases so does the mass, but two strings from different manufacturers of the same gauge will not necessarily have the same mass. The metals used, the size and type of core wire, the size and type of wrap wire could all be different. For example a silk and steel wound string has an average density lower than round wound, which in turn has a lower density than flat wound: silk provides bulk without much mass while flat wound strings don't have the air that surrounds round windings. Nearly all plain strings are made of high carbon steel hence have much the same density; thus most brands of plain steel string will have a similar tension for the same gauge.
There are factors other than string gauge, scale length and pitch that determine the string tension on your instrument. Assuming that the truss rod is properly adjusted, string height is the most significant but the string break-angle at the nut and saddle will affect perceived tension and to a lesser extent so will the stiffness of the neck and the guitar top.
Strings with higher tension will sound louder than strings with lower tension. As the distance they vibrate over is smaller you can normally achieve a lower action before you get fret buzz. Higher tensions produce cleaner, purer tones with improved articulation and allow faster picking.
Lower tensions certainly allow easier string bending but whether they are easier on the fretting hand is debatable as the lower tension increases the minimum string height possible. However at the budget end of the guitar market it is probably true to say that lighter strings are easier to play as the accuracy of fret height, neck straightness, fretboard camber variation and nut and saddle issues are likely to be the limiting factor in string height.
Classical sets are gauged in light, normal, hard, and extra hard tensions. Although the total pounds pull of classical string sets are lower than their steel string counterparts, string height, as measured from the fretboard, is set higher on classical guitars. This fact makes the tension difference critical.
Here's a handy string tension and gauge calculator we put together. It produces results very close to those figures produced by popular string manufacturers. Use it for example to work out what effect an altered tuning will have on the tension and what gauge string would produce a tension similar to standard tuning.
The note selection uses standard octave notation with middle c being written as c' and the octave changes on c. If you are unsure about what octave to select here are the standard tuning for guitar and 6 string bass in this notation.
Guitar: E A d g b e'
Bass: B'' E' A' D g c