Every raw processor uses:
- different underlying math (debayering)
- different default settings
- different scales/reference points for their sliders
- different math for what the sliders are doing
Consequently every raw processor will look different to start with and continue to be different no matter what you do with the sliders. You can certainly, through education and trial-and-error, learn to make each processor produce the best result (subjectively measured based on what you like/want/need) but you can never make one look identical to another.
If you like C1 you could use an older version of EOS utility to tether the Canon 5D and use Capture One's "Hot folder" capability to track the images as you shoot. It adds a 1-2 second delay, but often with that delay C1 will still be faster than alternatives. We cover hot folder tethering in our Capture One Masters Program