What is a pokemon's "Level" and its purpose?

Solution 1:

This level indeed indicates the Combat Power of your Pokemon. Higher level means higher CP. Each "Power Up" of your Pokemon increases this level with 0.5, but it cannot be higher then 1.5 of your current trainer level. If you catch a Pokemon, the level is random, that is why there is a difference between the two.

For this particular example, take the Pinsir with the higher level, as it will cost you less Stardust and candy to power it up. The lower one will have the same Combat Power if the IV completely match. Keep in mind that the moveset does not have to be the same, and can be a big influence. Thanks @Aequitas for this contribution