A true CAI which positions the air filter in the airstream (typically right behind the front grill), coupled with a higher-flowing exhaust can increase horsepower. However, it's main benefit is preventing a loss of horsepower because of high intake air temperatures. With an SRI, every time you shut down your engine for a while, engine heat builds up in the engine bay, so that when you start your engine again, the intake is drawing in heated air. The engine's ECU can change ignition timing to prevent knocking, but that can reduce horsepower. You can see how long it takes for your intake air to drop below 100 degrees F by installing a ScanGauge 2. My intake air temp reaches over 140 degrees F after an engine bay "heat soak", and it will take quite a while on the highway to bring that intake air temperature down.
My MX5 has a Mazdaspeed CAI. When I start my car after heatsoak, the initial intake temp at startup may reach 90F but quickly drops to ambient temperature when I start driving, even at low speeds.
The thing I don't like about true CAI systems is what happens during a rainstorm. The filter gets soaked and some of that moisture is getting pulled into the engine. It may not hurt anything if the engine is fully warmed up but I prefer not to take the chance. That's why I avoid driving the MX5 in the rain.