if the bulb used in the projector application is a higher wattage than the stock bulb, then yes, it will be brighter.
but if youre using the same wattage(say, 55w) H3 silverstar bulbs for a projector compared to 55w 9007 silverstars in a normal housing, the output will be the same brightness, the only difference being the dispersal pattern of the light. projectors are design to disperse light farther by projecting it, but by projecting the light farther, the area thats light up between the leading edge of the light dispersal pattern and the car might look a little dimmer. as opposed to a normal output lens, which lights up the ground brighter the closer a object is to a car. its hard to explain, something you have to drive with first hand.
then again, HID kit will give the dispersal of light as a projector lens will, but will make everything in the dispersal area just as bright as if it were right in front of the car.
i had projector headlights on my eclipse, i thought they were really bright, then i slapped some silverstars into the stang, and i think the stangs output and dispersal pattern are way better than the projectors i had.