To be honest, it's not that bad of an idea, for one, you won't be constantly comparing how the 120hz monitor looks to the ips and seeing the stark contrast in image quality 24/7.
You won't have to keep adjusting your eyes between 120hz and 60hz, 60hz will look awful and I imagine it'd do your eyes/head in having to keep adjusting.
While going with one of each has it's obvious benefits, best of both worlds, you saying you'd prefer them to be the same for aesthetic reasons, there are other benefits of going with two of the same.
Personally, the lack of input lag and the added gaming performance is way more important to me than colour accuracy, banding and whatnot so I'd go with 2 of the w2363d's personally if I was just getting 2 of one monitor.
I'm a one monitor guy though, I'd prefer just to use the steam browser or windows key out of games if I want to do something else. You'll get issues with point and click games too where if you go off the edge of the screen, your pointer will be on the other screen, I don't know, I don't see the pro's in having a second monitor at all but that's totally your call