Roseburg is more of a rough-around-the-edges blue-collar town, while Grants Pass is becoming, comparably, more and more civilized every year with the influx of interstate immigrants. Roseburg is solidly conservative, and Grants Pass is moderate with a definite libertarian edge to it. Grants Pass is and feels bigger and has more of a bustle to it, and also has more "cultured" things going on (even if they are quaint) than Roseburg does.
They both have similar roots as small Southern Oregon logging towns, but Grants Pass has turned toward the future more and is now more "cosmopolitan" (in the small, former Oregon logging town sense of that word

).
Basically, Roseburg still kind of feels like a logging town, like it didn't really leave the 80s, and I think there actually still is an operating mill there. Grants Pass just doesn't have that vibe so much anymore. Both towns have grown, but Grants Pass has grown more. With that has come sprawl, traffic, and worsening air quality. But compared to Boise I'm sure it's nothing.
The Grants Pass area is more beautiful with the Siskiyou Mountains right in your face surrounding the city, and is also closer to the redwoods and close to the coast. I also find the city itself more aesthetically pleasing than Roseburg. Not to say Roseburg isn't a nice place to live, but I prefer Grants Pass, personally. There is just more going on and it's becoming more liberal every year.
If I had to complain about Grants Pass, I'd say it's growing too fast and not in the best way possible. There is a Little Mexico neighborhood that is a little sketchy at night, and lots of cholos from SoCal (lots of Southern Californians here in general, for better and/or worse). I saw a skinhead about a month ago which was quite a shock, but I think that was an isolated incident of an outsider, because it's not a racist town at all. Also, it's still a fairly conservative small town with a fairly conservative small town attitude. The politics in the city are terrible... We just recalled all of our city councilors in a special election. They were crooks basically, but still.

Also, people in Eugene and Portland are friendlier than they are in Grants Pass, generally.
Roseburg might be a more quiet, laid-back place to live than Grants Pass now that I think about it, unless you relegate yourself to rural Josephine County...