I'll copy my guesses here, so maybe developers can make things more clear to us.
I read Resolve 14 Manual starting at page 135. There is a lot of info about Color Space Transform but seems no clear info about Color Science versions and their relation to Timeline Color Space. Also in manual developers name "Color Science" everything related to color transforms, not only Color Science setting in RAW tab. So probably we need some deeper lesson from Resolve developers to explain what going on under the hood when we disable Resolve Color Manage input and use "Color Science" options in RAW tab.
I usually use RCM + Color Checker correction, because when try to use Color Science it feels like always adds contrast and slightly clips extreme colors, so it slightly less flexible for future grading. But if you don't have Color Checker, using Color Science may help a lot to fix known dimmed saturation and brownish greens colors from BM cameras.
From my personal unconfirmed guess Color Science (v1, v3, v4) acts like input LUT with build-in color correction. Designed for specific camera and specific timeline color space. It is not able to transform colors to any desired color space same as RCM aka Color Space Transform do. If it produce ok result with some different timeline color spaces it only means that it just lucky similar to color space and camera that Color Science was designed for.
If shoot to ProRes, Color Science correction is baked in footage so you can not disable it or switch different version. That's why ProRes footage always looks more vivid compare to RAW.
Is this all correct?
I done a lot of tests this weekend and compare different combinations of Camera + Color Science + Timeline Color Space. The results are totally different and also very with different cameras.
Same tests with BMMCC footage. I only add here contrast 1.1 node and Color Space Transform node (Timeline to Rec709 With Luma/Saturation mapping ON) in the end.
BMDfilm (no Color Science) Colors converted from input to timeline with build-in Color Spase Transform. Uncorrected colors, brownish greens, less saturated look, 100% no any clipping, perfect starting point for ColorMatch tool correction.
Color Science v1, Timeline set to BMDfilm Nice looking image vivid corrected colors, seems no any clipping. Color Science perfect matches to camera and timeline.
Color Science v4, Timeline set to Pocket4K. More contrast and more vivid look, may start people to believe that it is "better" Clips extreme red colors with Pocket/Micro footage.
Color Science v4, Timeline set to BMD Broadcast. Seems no clipping but slightly washed blacks.
Color Science v4, but Timeline set to BMDfilm. Oversaturated Reds, something wrong in this setup.