Shoot 1080p30 on both cameras, unless you are shooting a lot of high motion scenes. According to the x920's specs, it does in fact shoot 1080p30, and given that you're shooting at about half the compression ratio with 30p (given half the frames to compress at almost the same bitrate) there should be a noticeable improvement in quality over the 60p, plus you get twice the exposure time for an equivalent shutter angle (i.e. better low light, though the 5D3 should crush it in that regard), which will likely be worth the lower frame rate unless there is a lot of fast action in the frame, plus no need to conform in post. As a sidenote, if you have a 5DIII, I would never use a 6D over it for video due to aliasing, moire, line-skpping, codec, lack of real MLV raw video option, worse ML support, etc. unless you absolutely must have a multicamera setup for punch ins or alternate angle shots of a talking head.
If you are, however, shooting high action scenes along with your sit down interviews, you consider shooting 60p on your x920 for those and stick everything on a 60p timeline, with the 30p footage being simply frame-doubled (automaticlaly, I'd imagine). As long as your 30p footage didn't have a lot of motion or was intercut a lot with your 60p shots, I doubt the casual viewer would notice the difference.
Although its a moot point, to get 1080p60 shot video to match the motion cadence of 1080p30 (assuming equal sensor characteristics, which is almost certainly not the case here), just shoot your 1080p60 video at a shutter angle of 360deg, aka a shutter speed of 1/60, and shoot your 30p video at the normal 180deg/1/60. Then, if mastering to a 30p timeline, conform your 60p video to 30p by simple 2:1 pulldown (dropping every other frame). However, again, either of the above make a lot more sense since you either get the advantages of 60p, or else better quality at a much more
If I were to shoot it, as long as I didn't have to run and gun a ton, I would shoot on the 5DIII as much as possible at maxed out bitrate H.264 for the interviews, and MLV 14-bit raw if you can afford it for the other shots, assuming they are not too extensive and you have the cards and time in post for it. It may sound daunting, and isn't for everyone, but even if you immediately transcode your raw files to ProRes 422 or the like you should see a considerable improvement in resolution, DR, gradeability, and overall IQ over even the highest bitrate H.264 output, since "1080p" on most of the Canon DSLRs is really closer to upscaled 720p than true 1080p resolution, and of course even with custom log-like picture styles you don't get the camera's full DR or really gradeabile footage. But I digress.