There is a key difference between the two owl species that I think explains this. Barred owls are "habitat and forage generalists," while spotted owls are "habitat and forage specialists." The barred owls preferred habitat includes a wider range of forest structure, and a structure that has become more common as Chromers pointed out in his post. The barred owls will also eat a wider variety of forage. These two attributes make it easier for barred owls to expand their range. The spotted owl is more demanding of habitat that is either old growth or older conifer forests, and have a narrower range of forage. I've heard they specialize on western flying squirrels, but I've never seen one of those, so it makes me wonder. Another attribute is that barred owls are larger and more aggressive than spotted owls, which makes it easy for them to expand into and displace spotted owls.