If you have the $1000 more to spend the 5D3 is great, but if not the 6D is a great alternative. We've been filming around moire issues for years with the 5D2 so saying the 6D isn't usable for shooting video is like saying a new Camry isn't drivable because it only goes just as fast as a Camry from a few years ago and not as fast as a new Lexus.
I've been using the 6D for video since it came out. My clients are happy with the results. Other shooters are constantly blown away by the low-light capabilities. If you absolutely have to shoot moire-inducing patterns regularly, and can't get around it by turning the in-camera sharpening off, tweaking focus, or pointing the camera somewhere else, you obviously know which camera to buy. Otherwise, if you can't figure out how to shoot a good video on the 6D spending the extra grand isn't going to help.
Moire is potentially an issue on any camera, just so happens the roof tiles hit the magic pitch to annoy your sensor. I get the same issue on XDCAMHD when I film anybody with a foxtooth patterned garment. I remember having to butcher a PL filter and fit some stockings in place of the glass on the first firmware version of the VX1000. And I combat moire regularly on my own two cameras and anytime I;ve used a hired 5D2.
So it's not an issue unique to the 6D.
I treat everything I shoot on a DSLR. Bare minimum is a half pixel guassian blur over everything. I can use up to 1.125 on something really bad.
Things that help:
Keeping everything progressive. From your transcoding or interpretation, to your timeline field order to your output codec, to your DVD or BR burning. Its a progressive camera, make sure everything else in the chain is progressive. Don't a assume. Check.
Marvels DSLR plug-in can help if applied with care.
If you have a locked off shot you can also selectively apply blur using garbage matting.
If none of this makes sense, then I've over pitched it. You may have got a dud 6D. You probably didn't. And someday you'll hit a fabric or texture that does this to your 5D3.
Like titokane said, learn to shoot around it, via on camera settings and or how to fix it in post.