No difference except a lightness to your wallet and more dirt in your engine. Having said that I have a replacement aftermarket filter but I've forgotten the brand name. I got it because it filters extremely well but I can wash & dry it then re-use it. Throttle tip in felt a bit better but that was likely me just thinking so. Since I have a tower strut brace changing the air filter is a pain so I chose this one that will last me the life of the car with little maintenance.
To put it in perspective, the Toyota Rally RAV4 uses the stock air box and filter, and they beat the competition. So I don't believe there's any advantage to having a cold air intake or washable filter.
I use the stock OEM air filter. It costs me $11.81 from Amazon. It says ACDelco on the box, but inside is an OEM Toyota filter made by Denso. I replace it every 15,000 miles whether it needs it or not. That works out to less than 12 bucks every 2 years. I see no advantage to an aftermarket washable filter.
I've had a little different experience with my short ram air intake. Before and after installing I ran the same trip from Colorado Springs to the Denver Airport.
My first trip running stock at 70 mph ( I'm sure I was driving people nuts!) I made a solid 31.4 mpg. My second trip with the ram intake I made 33.3 mpg. Was it worth 1.9 miles per gallon or 24 extra miles a tank. I don't know. I do know I also climb the same hills in higher gears.
Like most have stated on this post, the oiled aftermarket filters should be avoided. They really are not going to do much by themselves as it is the flow path that drives most of the restriction in an induction system. They also do a very poor job of filtering. I know this from experience as I designed induction systems years ago when I worked for an OEM supplier and we tested a K&N filter against our production filter. I don't recall the numbers now but I remember being surprised at how low the initial filtering efficiency was compared to the OEM filter and the size of the particulates that got through. I wouldn't install one on any of my cars. Plus if they are not oiled properly they will let in even more dirt if under oiled and potentially foul up the MAFS if over oiled. Just not worth it.