Checking out on Delta via my Delta AmEx allows me to simply login to my AmEx account (saved via a password manager) and checkout without entering my actual card info. The convenience factor there is definitely nice.
Depending on what they mean by "Customized Experience", and what data does this allow access to, it may mean better integration with a number of consumer finance apps, such as Mint, YNAB, etc. Doesn't seem like it from the description in the website, though.