If all you're doing is what you wrote, I'm not sure any of the two are right.
You're integrating raw files without aligning first, so the result is always going to be bad. Plus, if you feed the CR2 files to ImageIntegration, you'll stack bayer coded files, which will give funky results.
The correct path is either use BatchPreprocessing from the CR2s or after you've converted them to fits, or do it all manually by using a lot of tools, which I don't recommend.