If your country is spying on you, it can use the data it gathers against you in a court, etc. If it's a foreign country, what could they possibly do?
Since you're not a citizen of that country, use the information in your email in far less scrupulous ways? Perhaps they could blackmail you into being a foreign intelligence asset. Perhaps a corrupt employee could slip your information to a criminal organization who will then steal your identity.
All of these things seem rather unlikely, and chances are you're equally boring to both governments. But your assumption that the government of a country you're not a citizen of will treat you better than the government of a country you are a citizen of seems pretty odd to me.
The NSA, as secretive and as evil as it may become, is still a US government agency run by Americans with a moral code. The same cannot be said for the KGB (colloquial for FSB), Russian government, or Russian organized crime (all three of which are pretty much inseparable).
It's far less likely that they'll care about you but if they do notice something that they want, you're fucked.
More generally, anything that nobody has ever seen happen is unlikely.
I have heard of many occurrences of a government profiling, targeting or even suing their citizens over national security. I have never heard of anyone having their identity stolen by a criminal organization who got it from a foreign nation's government.
If you are in danger from a foreign government reading your email, you are an employee of your own government.
I feel the same way about NSA surveillance at this point, on Tuesday June 11, as I do about airport security: it's ineffective and offensive, but not the start of the decline of the Republic.
Let's vote this gal/guy into office so we can have our rights suppressed in the name of freedom, said no one ever.
See links to primary sources, including David Kravets: