more pixels/inch = more stuff gets in the way of light = dimmer display
You would think so, but it turns out the pixels themselves are what actually let through the light from the backlight.
But because of limitations in how small we can make the 'stuff' besides the pixels, basically the structure and circuitry, a higher pixel density display usually ends up with a lower percentage of it's total area devoted to pixels letting light through.
That's why the iPad 3 had to have a bigger backlight and thus a larger battery.