Okay, what are OEM parts? "OEM" stands for "original equipment manufacturer". In practical terms, this means the party that made the original part for your car be it the muffler, bumper, clutch or whatever. Isn't this part just the car company selling the car be it Ford, BMW or whomever? Nope. Most car companies outsource much of the car part manufacturing to smaller companies.
This outsourcing is why the bankruptcies of General Motors and Chrysler have such far reaching impacts. Not only does it impact everyone at those companies, but everyone at each independent company that makes parts for GM and Chrysler. If these independent companies lose enough business, they may have to shut down. This is problematic since they also make parts for other brands. This is also why the idea that a Ford is "American made" and a Toyota isn't is mostly hogwash. All the brands are getting a lot of their parts from the same suppliers whether they are in the United States, Canada, Mexico or wherever.
Aftermarket car parts come in two variations. The first is simply a generic form of the OEM part, much like generic pharmaceuticals compared to name brands. The second is an accessory for a car such as cold air intake systems for the engine, racks to carry bikes and so on. There isn't much debate that this second form of aftermarket car parts is fine, but the first variation is the area where contention starts.
OEM parts are almost always more expensive than aftermarket car parts. That being said, the price difference often isn't that large in many cases. This is important because OEM parts are generally better for your car than aftermarket parts. The issue is not the manufacturing process of the aftermarket car supplier, but the simply fact that the OEM part is made using the same molds and manufacturing process of the original part on your car. This means it should fit perfectly whereas the aftermarket part might not be an exact fit.
So, which should you go with? It depends. Aftermarket is definitely the choice when it comes to improving the performance on your car. If you are just looking for a part replacement, OEM parts are going to be slightly better although more expensive. Only you can decide if the price difference makes the aftermarket car parts a better deal.