I agree with both Chis's on some points each.
I have seen testing done on a Scion tC where they added a TRD "Cold air intake". Made 1 whp improvement. Basically nothing worth the money nor improvement over stock.
I have seen 1GR motors add a TRD and pic up 7-12 whp. Can't remember the torque.
Thus the improvement would be seen to come from not only the flow of the air filter
, but also the design of the intake. With out there being a substantial difference between the aftermarket and the stock, there will not be much of a gain to be had.
The motor is going to pull in air. Put your hand, per say, over the throttle body (huge restiction) and you can eventually stop the from a lack of air.
On the extreme other end, remove your hand completely. It will breathe much easier and efficiently. In all actuality that is the purpose of the thottle body disk.
With that in mind, put a very dense perforated material over the throttle body. It will be, inturn, hard again for the motor to breathe. Take it away, and it will breathe freely again. Simple yes.
Now, I know that all of that seems like redundant common sense, but it is still lost to many. My eaisest example, of self, is my turbo kit.
I had a filter on that was from my days with a rear mount setup. That filter would continuously get extremely dirty. Well I had to put it on my front mount so that I could have a filter on, unitl my new one came in.
I had cleaned and cleaned that old filter. Looked good to the eye. But as soon as I did my first test drive with that filter on, versus before with no filter, my truck was immediatly sluggish compared to without a filter. Couldn't breathe well enough, to get the volume of air in fast enough, and thus my boost even came on about 500+ rpms later. Shocked me how badly the performance was with just a filter.
Needless to say, that when my new filter arrived and was installed, the truck got the performance back that was nearly identical to not having a filter on at all.
They do make a difference, but it depends on many things that vary between vehicles.
So, a restriction with a thinner volume of air will have a much greater impact than a similar restricion with a much denser volume of air.