EDIT: Fat clients
This is where Apple's and Google's respective computing strategies start showing their strengths and weaknesses. Apple has put a lot of effort into creating the best "fat" client platforms around. From iOS to Mac OS X, the majority of the functionality exists at the endpoint, augmented by optional cloud services with fairly narrowly-scoped purposes.
By contrast, Google delivers an end-user experience by pushing their platform closer to end users. Google operates on the basis that the network is cheap (RIP Sun, "The network is the computer"), and that it can economize by providing functionality at the data center.
I'd argue that Google reflects a more modern way of thinking, and that Apple's approach is somewhat anachronistic. However, as far as surveillance goes, Apple is perhaps at an advantage. All things equal, it's easier to attack a few datacenters than to individually attack millions of reasonably secure endpoints.
This is doubly true when we consider business models of the two companies. In order for Google to monetize your information, it needs to see your information in some sense. That makes Apple's business model of mostly doing cost recovery through device sales even more beneficial in a surveillance-averse world.
EDIT 2: If Apple wanted to be proactive about divesting Google from some of its monetizable data collection, it would extend something like iMessage encryption to Apple users on Gmail. Send email from Apple's client to another iDevice user over gmail? Give them the option of encrypting it. Don't let Google peek in.