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If you are mature enough to stand the thought of being seen with that particular person outside of the workplace, take them for dinner and have a chat about what it is that is bothering you both.
You might just find that its a severe personality conflict, and that perhaps you have a lot in common.

I once worked with a woman, and we couldnt see eye to eye on any matter at work. We had similar opinions, but both wanted it done ‘just so.’
However as soon as the door was closed, we were fine.
Best way to think of work is: Work is work, once you’ve finished that’s it, leave it there. It’s a healthy way of looking at worklife, and in time you will come to understand eachother better.
We often met in the weekends, partied, brunched. Because we respected eachother as people. Thats what you have to do, even though you dont see eye to eye.

Usually both people need to take a couple of steps back and look at the big picture.

If you are wanting a more catty and extreme workplace warfare approach just make their life a living hell until either they quit or you get fired. (Dont really think that this is an ideal method though, but it depends on what final result you want).

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