In what sense?
I think the former situation creates a legitimate expectation of privacy. I think the latter situation does not. Which is why I use Apple Mail instead of Outlook for iOS.
And yet somehow there's always someone saying, "well, you let Gmail employees run programs that aggregate data over its contents, therefore it's not really violating your privacy when a government investigator looks at them without a warrant". Which is it?
Now, Google has a 4th amendment right with respect to "your" mail sitting on its servers, even though its employees have access to it. Because it's really "Google's mail," stored on Google's property, under Google's control.