I think it depends on the brightness of other light in the room. To reduce eye strain you should try to keep your screen at a similar light intensity compared to the rest of the light in the room.
A particular study showed that eye strain was increased when watching a bright screen in a dark room.
"The result of all this testing and observation was that there was less eyestrain, discomfort and visual fatigue when the volunteers watched the movie against a lighted wall. "
For my self, I try to use more ambient lights that point at the ceiling, or by pointing a desk lamp at the wall behind my monitor, so it smooths out the light and doesn't make one spot so bright. You can also find LED lights that stick on the back of a computer, which point at the wall, to increase the amount of ambient light in a room. Try to keep the screen not too much brighter than the other things in the room.