New member, can't comment but I agree with these answers. As a gamer I would like to see my "global" rank on a game that is cross platform. However as a Software Developer I understand why they are separate.
The first thing that comes to mind is the fact that they are different companies (what @JoshPetrie mentioned). Microsoft has their own servers and databases while Sony has theirs. Since they are separate companies with separate data hubs, there will naturally be separate rankings. They would have to work together and share a system that houses both datasets. That doesn't seem likely because that would mean that Microsoft has access to Sony's data and vice versa. And nothing is more personal to a company than their data.
Let's assume however that this were true and there was a shared database where all the rankings are together. I bet the rankings wouldn't be as evenly distributed as one might think and it would be due to hardware differences which result in a big difference in the ability for a user to master the game. Each gaming console is a different environment, or medium, in which the user can play the game. Based on its design, the environment creates limitations on "how well" the user can play with respect to users on a different medium.
The biggest example I can think of (and was already mentioned in another answer) is the difference between Console and PC.
Let's use Team Fortress 2 as an example. The console version is played with a hand held controller. Usually the contoller is operated with both thumbs and index fingers (4 digits, at least how I play). The PC version uses the keyboard with W-A-S-D movement, other keys for functions, and the mouse (6 digits used at once, by my count).
Not only are the "controllers" different, but, like @ratchetfreak said, each system has its own degree of performance power. So the exact same game could be slow and laggy on Xbox, but very fluid on PS or PC.
Also PC's can be upgraded as opposed to console games which are static until the new version comes out. Which then the leaderboards would be different since a newer version of the game is required (which means a different server and database and blah blah...)
On top of these differences, you also have system settings like mouse speed which can be increased higher than joystick sensitivity (which, for me at least, makes up the biggest advantage of PC gaming).
Many other factors are involved I'm sure but these were the first things that came to mind when I saw this question. Sorry for being long winded, I got excited and blurbed it out as fast as I could.