There are a few variables to consider (just in my opinion anyway).
If your talking about a straight swap of factory paper filter on a naturally aspirated petrol engine for a re-usable K&N type, based on my personal experience the main benefit is long term cost savings. Specifically, the cost of replacing paper filters Vs cleaning and re-using K&N type.
If you are looking for an increase in performance (and often a reduction in fuel consumption) then it depends on the age and make of vehicle as to how to proceed, but generally speaking you will need to do two things. 1. Get cooler air to the engine and 2. Increase the surface area of the filter to ensure maximum air flow. If you decide to go down that route, often a new filter of a different size and shape will be required, so people often go the re-usable route at the same time.
I drive (actually I have no idea what the US equivalent is) but lets just say a Corvette engined sedan. (a 5.7L LS1 if u know ur engines, running a very conservative 235KW). I tried swapping the large factory paper panel filter to a K&N style a friend had and saw no difference in anything. Then I performed a few modifications to the air intake system ensuring that hot air from the engine bay wasn't being drawn into the intake, and instead cool air is being forced in from behind the headlight, and replaced the tiny 2inch ID breather pipes with two 4inch pipes. Woah baby. MUCH more induction noise above 2900RPM and noticeable increase in power.
Many years ago I also ran a 351 Cleveland V8 force fed by a Garrett T4 Hybrid blowing through a modded 650 Holley. As this was the days before turbo charging was popular outside diesel's, almost every part was hand made. With all those custom parts, my air filter of choice was.........a giant tube style paper filter from a truck. Cheap, easily available and with about 500HP and 500ft pounds of torque under my foot with a rich mix and no water spray, I'd say it's performance was acceptable. (No intercooler either)
I did run K&N branded filters on my "dirty" car though. I had a 70's Corolla that I used to belt around the bush (err forest) in amateur rally events. 1600CC with Weber side draft carbs. In off road use I totally recommend those types of filters as you needed to clean the filters after every race as a result of mud and dust and oil etc. Also there was no real "standard" air filter for that setup.
Finally (and I know this is long, but I'm killing time at work) be wary of Pod style replacement setups. They are as common as anything in the boy racer scene because they look cool and give you massive induction noise. You'd rarely see them on a race car though, because they suck hot air from the engine bay. As any real racer will tell you, hot air has less O2 and less O2 means less power. In a carb'd car this means your likely to be running rich (unless you tune your car as well) which will make your fuel economy worse. In an injected car it's likely that the computer will adjust your mixture to compensate, but you'll likely develop less power than a clean filter in the factory setup.
So yeah. Long story short, they may save you some coin over the years, but only in filter costs, not fuel.
This has been my 0.2c
