I have not seen any brands hallucinated. The biggest issue was the math as you pointed out. I created an if-then-else if statements in the prompt to force the use of code/Python for calculations.
The free version of Gemini functions less well than the others because it executes my instructions less rigorously, but I have not seen product prevalence over others. I'm also not sure how I could track though without running the same case study several dozen times to see if anything statistically significant comes ups or changes.
At the end of the day I would say my idea is best for getting you from 5% knowledge on a topic to an 80% level and a much more advanced and objective place to make a decision and finish out with your own "eyes-on" research.
Most of the language I use in my prompting is structured around weeding out hallucinations. At each step along the way I ensure I'm asked to confirm the previous step's output.
The balance I have been trying to find is between "show me all you work" so you know the math is all there and correct (and perfect for enterprise) and then trying to tell friends or my parents who don't care to see the math (the background) that it needs to be there for this to work right. I have seen scores "ballparked" by ChatGPT. The rankings didn't change in the end, but the scores were a couple tenths off.
I've used ChatGPT 5.2, Claude and Gemini, but have never switched between steps which sounds interesting! I have found the same as you with Claude. ChatGPT is a close second and Gemini doesn't give me the type of response I'd prefer to keep things smooth and traceable. I'm looking to buy a new car right now and each of the 3 models has given me the same top 3 each time so I find that as re-assurance.
The free version of Gemini functions less well than the others because it executes my instructions less rigorously, but I have not seen product prevalence over others. I'm also not sure how I could track though without running the same case study several dozen times to see if anything statistically significant comes ups or changes.
At the end of the day I would say my idea is best for getting you from 5% knowledge on a topic to an 80% level and a much more advanced and objective place to make a decision and finish out with your own "eyes-on" research.