Strictly speaking you should get better results with the mirror as it won't absorb as much of the light as the white material will, however it depends on how the mirrors are arranged and the direction of the LEDs. One setup may provide more light at the center while the other might provide more overall light but spread out over a larger area so it will read as dimmer even though the overall output is higher so how you measure the brightness is important, and that depends on what you're intending to do.
Just a side note, most LEDs are not very good broad spectrum light sources, they might look white to us but if you've ever seen the spectral output of one it's VERY peaky, and the color rendering index (spectral flatness) is only about 75 for a common white LED, you can get higher, probably in the 80s if you buy more expensive LEDs designed with better phosphor blends, but if you need a true broad spectrum light source halogens are much better. Don't know if that's important to you but the title of the thread is the science of color.