Why not both? I've seen and heard of people who are born with brown eyes desperately wanting blue eyes, and I've even run across some situations where people who have nice, natural blue eyes really would rather their eyes be brown.
Fortunately for all situations, these are both possible.
Colored contacts can take both people's eyes and turn them into the exact color they were thinking about.
The cool thing about getting colored contacts is that you aren't stuck with them.
For instance if you dye your hair, it's stuck that way until you either shave it off, or dye it another color.
With contacts if you don't like the color, you take them out and you're done.
If you are looking for brown contacts, it doesn't have to mean you don't already have brown eyes.
Some people have dark brown eyes and just want them a little lighter.
Some people with light brown eyes want to know what it's like to have them darker, etc.
If you have blue eyes, maybe you've spent your whole life wondering what it would be like to have dark puppy dog eyes, well now you can.
What's cool is that you can get these colored lenses in prescription of your choice, so you can change your eye color and improve your vision at the same time! It is very important to remember that if you do plan on going this route, even if you have perfect vision, a prescription is still going to be required.