What makes an air filter better or worse than an OEM air filter at removing debris and reducing engine wear?
I would say stick with your OEM air filter if you don't want to think about any possible problem, and you "don't" need performance. Let me explain in details.
Performance Air Filters (won't be giving brand names):
They increase the air flow to the engine, so the car performance is increased. To increase air flow, they generally use cotton or foam filters, which means more dirt/dust will also come. And for filtration, they use oil to store the dirt/dust, etc. Although they claim that filtration of their systems are better, it is not. I will explain why under OEM Paper Filter Section.
Advantage of cotton filter is, some of them are lifetime guaranteed as they are claimed, so you just wash/clean and reinstall it so in long term you won't be paying more for air filter. Of course don't forget applying filter's oil again.
OEM filters and other Paper Filters
What can be done to let the air flow, but minimum amount of dirt passed through? Reducing the sizes of the microscopic holes on the filter. OEM/paper filters have a balanced number of holes and proper size of them to ensure the best protection while letting the air flow. That is why paper filters are letting less dirt/dust in them. It is a comparison of cotton and paper with their specific layer properties.
If we are talking about a regular street car, stick with OEM paper filter.
OEM/Paper Pros: reduce engine wear, better filtration
OEM/Paper Cons: regular maintenance, not reusable
If you just like the sound (of Cold Air Intake), and you really need a performance gain, buy the best brand available to make sure that it will cause the minimal harm.
Cotton/Perf Pros: reusable, increase in performance
Cotton/Perf Cons: worse filtration which means faster engine wear, costly if not planned on long term use because they are reusable
I've got a BMW F30 car and I am currently using stock filter. If I want to increase the performance someday, I would spend a lot of money on advanced filtering techniques to gain the best performance while trying to maintain the protection as much as I can. Worthy or not worthy? It is up your preference. I don't find it to be worthy at the moment since this is not a race car.
I'm not sure if I'm allowed to give links as answers, but this is the best I've been able to find... although it's a decade old. Anyone have a newer test?