Nothing, not even Cinematch (despite the marketing claims), will automatically make two cameras look the same.
Best you can do is to adapt the OETF + color space of one camera to the OETF + color space of the other camera, and then manually adjust the image from there in linear (and, of course, shooting color charts will help with that manual adjustment) . Or move both cameras source OETF + gamut to the same intermediate color space (by using ACES or RCM), but even then you'll still have some work to do to match the temp/tint and the exposure in the intermediate working space under the ODT.
If you want to do the former and adapt the OETF + color space of the 4K Production camera into the OETF + color space of ARRI, this screenshot shows how to setup the color space transfdorm (assuming you shot in BMD Film mode). From there you will need to manually match the temp/tint and the exposure of both cameras and can then apply the same transform from ARRI LogC AWG to BT.1886 (or whatever other reference display standard in which you're viewing the image).
- CleanShot 2021-10-11 at 19.29.03@2x.png (102.5 KiB) Viewed 1392 times
If your goal is to match the two BMD cameras, the easiest way is to use Resolve Color Management in Resolve v17. Just make sure to tag the input color space for the 4K Production Camera correctly. If you need to check the color space and "gamma" setting for BMD camera clips that info can be found in the metadata panel of the Media Page (and, by the way, BMD unfortunately persists in using the incorrect label "gamma" in Resolve for what are more correctly called OETF and EOTF — Opto-Electronic Transfer Function and Electro-Optical Transfer Function).
BRAW files will always be tagged correctly by default in RCM.
If you've never used RCM, this excellent training title by Alexis Van Hurkman explains in detail exactly how it works and how to use it.
https://www.rippletraining.com/products/davinci-resolve/color-management-in-davinci-resolve-17/