Yeah, there are differences for sure. Some situations show larger differences than others.
One theme is that the Panny versions are much more saturated in skin tones than the Alexa. Coming from the kings of colour science, this has got to be deliberate, so even ARRI aren't trying to match the Alexa.
I think that instead of asking "are they identical", the better question would be "does this impart some magic".
I mean, everyone agrees that ARRI has the magic but their cameras don't even match each other between sensors, so it makes no sense to have a higher bar for the Panny version than we'd apply for ARRI themselves.
My impression was that the ARRILogC profile and the ARRI709 LUT is the most like the Alexa, with the V-Log -> CST -> ARRI709 LUT not being as good. This makes sense as whatever colour / gamma secrets ARRI applies in-camera can be put into that profile as it's customised to the Panny sensors and also safely locked inside the camera away from prying eyes (unlike anything they put in their LUT).
However, the Alexa also responds differently in the spatial dimension, with the far-red response including a more spatially distributed response from skin tones. We also know that Alexas process the image spatially in-camera due to their texture options and processing. Who knows what is going on with texture in there. IMHO the texture of Alexa images is right up there in importance as their colour response.
None of this includes temporal aspects either. While I struggle to think of what processing might be occurring in-camera between frames, there might be some (we can't tell), and that's beyond the possibility that the hardware itself has some sort of secret properties that contribute to the image.
FDTimes did an entire episode on the Alexa 35, with interviews of over a dozen people and 100+ pages:
https://www.fdtimes.com/pdfs/free/115FDTimes-June2022-2.04-150.pdf
Here is the image pipeline in the Alexa 35 (page 59):
To give some idea about how stunningly out of our depth basically everyone on the internet is who talks about this stuff, starting on page 116, Dr. Tamara Seybold talks about Textures..
"For example, the debayering already needed to obtain the full color image doesn’t only generate RGB values but also influences the perceived sharpness and grain rendering. And many more steps influence the clarity and grain that are important aspects of the texture of an image. So we, in the image science team, pushed hard to obtain the best results by really optimizing each and every step in the image processing pipeline, not only for the best color rendition but also for the best texture, as we call it. We did that in a holistic way, optimizing steps in the beginning of the pipeline together with later steps so that the overall result would be best. At some point, this came down to having more than 30 parameters that we had to optimize together—a huge amount. We specifically had to build a small “texture grading machine” to be able to optimize all these parameters together."
(emphasis added)
I don't know about anyone else here, but I would struggle to even list 30 parameters, let alone identify all the parameters, isolate the 30 that matter, then find the sweet-spot (or sweet spots) in a 30-dimensional space.
This is regarding the Alexa 35, but I remember reading in there somewhere that the innovation of the Textures feature is that you can choose different profiles on the new camera, whereas on the old ones you only had the one, and that on the previous models they had chosen a texture configuration that was their best attempt at a one-size-fits-all. So the inference was that the previous cameras were also doing this kind of processing.
By implementing their colour science inside the camera, they could be doing all sorts of stuff. They could have things that analyse the image and then apply different treatments depending on the scene the camera was capturing. They certainly have a team capable enough and a camera with enough processing power to have a dozen, or a hundred, or a thousand, LUTs or algorithms inside it and be changing these things based on context or WB setting or sensor temperature or whatever the hell else they found was useful.
The sheer depth of knowledge that has gone into their image science is incredible. In 2009, Glenn Kennel joined ARRI as their CTO, which was a new position at that time, and in 2010 he was promoted to President and CEO. Glenn had previously worked for Kodak from 1980, and worked on various things that involved the gradual digitisation of the pipeline, including things like telecines and film scanners etc. My understanding is that his contributions at ARRI were pivotal for the development of the Alexa, which was the first digital camera to gain wide acceptance within the industry and did so due its film-like response.
A bit of searching revealed some interesting discussions we already had during lockdowns..