I've had great experience with Michelin Defender LTX M/S's on our Yukon Denali XL's and Escalade ESV's with performance and mileage in year-round use in Ohio.
My only personal experience with the Michelins Cross Climate2 was in a newer Acura MDX we drove for 2 days that had a set of these tires. Much different vehicle platform than our full-size SUV rigs so not sure if it's an "apples to apples" comparison... The Michelins Cross Climate2 were absolutely fantastic in moderate rain. I was proactively trying to hydroplane and couldn't rolling down the highway at 85+. I did think they rode a little stiffer than the Michelin Defender LTX M/S. But that could also be based on different tire sizes and maybe with smaller sidewalls than the 285/45R22?
As I'm sure you know the original LTX M/S have been discontinued and replaced with the Defender LTX M/S2's. They appear to be pretty much the same tire, with only a very slight change to the tread pattern if you're paying close attention.
Just put a set of Michelin Defender LTX M/S2's on the wifes '19 Escalade ESV Premium today.
I really don't think you can go wrong either way. Just looking at the two side by side the Michelin Cross Climate2 is severe snow service rated with a lower mileage warranty. So they may perform better in rain and snow, not last quite as long, and also maybe ride a little stiffer than the Michelin Defender LTX M/S2's. That being said I think the pros and cons or "differences" are probably marginal for each.