Depends on the car. On a normal passenger car there will probably be no difference.
On a high horsepower car it will make as much as a 30-40 HP difference at the wheels, especially on a blown car with a supercharger or turbo system under higher boost levels which force the engine to 'suck through a straw' on the factory intake.
Two ways an intake "makes" (or rather provides means for producing) more power.
First, it's less restrictive and higher flowing which makes a difference under heavy loads and high RPM only. If the engine air intake needs are not that drastic (non performance oriented engine with a over safe and conservative factory tune) and the original intake is sufficient at all RPMs, there will be no difference.
Second, colder air from outside the engine compartment is denser than the hot under hood air and allows more fuel. But more importantly colder air is less prone to detonation ('pinging') and allows for a more aggressive tune with more timing which creates more power. A true cold air system draws air from outside the engine bay. The ones you see with just a tube and a under hood filter are not CAIs and should not be labeled as such.
Here is mine:
http://jlttruecoldair.com/zencart/index...oduct_info&cPath=1_7_20&products_id=45
Some things you want in a CAI:
1) Draws air from outside the engine bay, from a sealed opening so that no under hood air can enter the filter
2) On mass airflow systems that use a MAF meter, you want as much straight tubing leading to the MAF as you can to get laminar air flow over the sensor. Bends directly in front of the sensor cause turbulence and lead to poor and inaccurate readings and make it impossible to tune properly. On speed-density systems that use a MAP and IAT sensor, it?s not a major concern other than bends cause frictional loss in the flow path.
3) Single piece design with smooth inside walls and constant diameter (ie: mandrel bent/molded). Ridges and mold lines on most factory tubes cause turbulence. Air that circulates in endless circles is not entering the engine and is occupying inlet space that useable air could be flowing through. It also heats up the air via friction. You do need some kind of flexible coupler in the system though, as the engine moves under hard acceleration and the inlet is fixed to the fender well. If the tube is a single piece of metal or plastic, you need some kind of rubber coupler that will flex or something will eventually stress and crack.
4) Ease of filter changing and location. Some of them may relocate filters to impossible locations, etc. Also the location of the filter in the fender well is prone to sucking up water in heavy rain or when driving through shallow water, which will pretty much destroy the engine. Water doesn't compress; the metal in the rods, main bolts, crank, and head bolts will yield first because the water will not compress under any circumstances. This is what is known as hydrolocking and would be the same thing as trying to run 10000 lbs of boost.
Some CAIs like the one I linked change the position of the MAF from the factory position relative to the filter and the throttle body requiring computer and/or MAF sensor recalibration (i.e.: you'll need a new tune to compensate). MAF sensors are so precise which makes them sensitive to changes and very tricky to work with and require custom computer tuning for optimal performance and mileage.
As for filters, larger filters conical filters with surface area on both sides provide more surface area and require less work for the engine to pull air through. But again, if you can hold the throttle open and you don't see or feel the intake tube or filter wanting to collapse or move at all under the vaccuum in that condition, it's probably not going to make much of a difference.
All in all the intake itself doesn't make power, it's just a small piece of a much larger system, which on a engine with other modifications like blower, turbo, large cams, free flowing exhaust, etc. can quickly become a restriction.