Snowden took only documents that describe the overall global surveillance infrastructure.
Snowden had access to raw data streams for almost all SIGINT operations. System administrators like Snowden received special "root access like" clearance called PRIVAC (Privileged Access) where people allowed to be exposed to information of any classification, regardless of what their position actually needs, apparently because they are sysadmins and need to see what's going on. Snowden had 'technical' access to live feeds for all active operations, drone feeds and other information regardless of classification all over the world was wider than anyone participating in operations had.
It's not hard to imagine that there are other people with PRIVAC access who are actual spies. Just by observing important stuff and not taking anything compromises the system. If they downloaded some of that stuff, it has been open doors all this time.
Only after Snowdon's revelations NSA has added the two-man rule for sysadmins. Apparently it was too costly before. Increasing the data collection was more important than building the system.
I think there is systemic failure in US/UK intelligence organizations. They constantly emphasize offense over defense even when they know that they are very vulnerable. It's hard to show results for good defensive posture.
People ... need a years to develop, and could potentially provide useful service for decades. Having an entire cohort of agents removed is a substantial blow.
It's something that I've wondered about for a while now, but really, who am I to question such things?
So I think the strategy is much different and much more durable now. The military designs ciphers to be resistant to theoretical future quantum computer architectures. They fund research every year to prove various properties of crypto systems. And I'll bet there are lots of fallbacks for any critical infrastructure.
This OPM hack is probably the most damaging for the US government's spying efforts, even more than the Snowden disclosures.