This is my first post on here but after reading the thread it strikes me as odd that not one person has mentioned pressure drop? and most people seem just to be talking a load of hot air!!
(sorry I though it was a good one anyway!)
Surely this is just as important if not more so than the dreaded heat soak everyone keeps talking about.
Using basic physics you have 14.7psi of pressure forcing the air into the cylinders, if you have a standard airbox with all the little resonance chambers in that help to reduce noise and the torturous route that the air has to make from the front of the car through the ducting through the airbox, through the filter and then 90deg into the inlet then you can easily lose a couple of psi in pressure drop.
Thats the same as having a turbocharged car and running 18psi of boost compared to 20psi of boost, i.e a noticeable difference. Using a open filter with either a short ram intake or a smooth curved inlet pipe is obviously a lot less restrictive to the flow of the air merely from the fact that the air has about half the distance to travel through and without any major restrictions. The air may be slightly hotter yes but if it is ducted well and has a nice supply of cool air from the front of the car then I would find it hard to make the case for the standard airbox and ducting making more power as it is just physics really.
Also the above comment made about that impreza being turbocharged and that is why an open filter helps is a very strange view. Tuning N/A and FI cars is exactly the same, I don't get why people think they are different, its just like having a car on a different planet where the atmospheric pressure might be 2 bar rather than 1 bar!! They still work in the same way. The only real differences are in cam choice and exhaust sizing.
At the end of the day though regarding induction kits, with my car the open filter transforms the way the car sounds and feels which makes the experience of driving the car so much nicer for me. Its not a race car so every 10th doesnt count so whether you lose or gain a couple of bhp doesn't bother me, surely if you get more enjoyment out of the car then thats the main point?