The LA Times conducted a test that pitted a silpat against parchment paper in a holiday cookie bakeoff. (I'm not going to get into the fact that the article also states that "traditionally, careful home bakers have used clarified butter when greasing is required," though I have yet to meet a home baker who "traditionally" has done this.) They concluded that, while both parchment paper and silpats performed better than "untreated" pan in terms of spread and even cooking, the silpat performed better than the parchment paper in two out of three trials.
This is not a very fair test for the simple reason that the two things, although they share some of the same functionality, are designed to do different things. Would you compare a fork and a spoon, both useful utensils, and declare the fork to be superior because it is more proficient at stabbing food with its prongs?
A silpat is good for preventing spread, as the LA Times discovered when the baked shaped cookies. Everything will cook more slowly and evenly due to the extra insulation the liner offers and almost nothing will stick to it, not even candies and caramels, if you like to make them at home. Parchment paper's main purpose is to keep baked goods from sticking to the baking sheet and keep the sheet clean. It may aid, in a small way, in even cooking, but it is not going to insulate everything like a silpat does.
While the Times seems to suggest that the silpat might be better overall, parchment is a better choice if you can only use one. Parchment paper is much less expensive than silpats are and if you have multiple cookie sheets, you'd need multiple pads to cover them all when baking cookies, for example. You don't need the extra insulation for the simple reason that the vast majority of recipes are not formulated for use with a silpat; they're made to work with a regular cookie sheet or a parchment-lined one, since the parchment will not dramatically alter your results or baking time. Additionally, you can't line a cake pan with a silpat and you can use parchment to make piping cones for icing, as well.