I have the same problem, on a 5DmkIII though. I have back button focus instead of the shutter button. When I'm not focusing in AI Servo it shoots around 3fps. If I am focusing it shoots at the normal 6fps. The 1st and 2nd image priority is set to focus. If I change it to anything other then focus it might pause at the start but does shoot at the full 6fps when focusing and when not.
Its odd because it is slow when not focusing, but normal when it is and only in Ai-servo.
After further review and confirmation in the manual. I have deemed that this is a feature and not a problem with the 1DX or 5DIII.
When you select 1st image "focus" priority and 2nd image "focus" priority the frame rate does slow down dramatically to ensure focus.
After further testing, "it appears to me that the 2nd image focus priority choice," has a greater impact on the shooting speed then the 1st image selection choice does.
"If I select 1st image focus priority, and 2nd image focus priority, the fps rate slows down."
"If I select 1st image release priority, and 2nd image focus priority, the fps rate slows down."
If I select 1st image focus priority, and 2nd image release priority then the the shooting speed is "fast."
* "So, it appears that the 2nd image focus priority choice slows the frame rate down more than the 1st image focus priority choice."
I have the default equal priority set for 1st and 2nd image and that seems to be working very well for me.
There is also another setting on the next menu: AF3:One Shot AF release priority, and I have that one set to "focus priority" which is also the default.
This One shot setting, coupled with the 2nd image focus priority choice, may further explain why some were getting different fps rates depending on which AF mode (One Shot vs. AI Servo) they were in.