It's a bit more nebulous than that. The Snowden leaks covered a collection or different programs between the NSA and GCHQ which took place over several years. Some of them began under Bush, some of them began under Obama, some of them were expanded under Obama, some of them Obama lied about shutting down...However, there was a huge expansion of American meta data being collected under Obama, even though candidate Obama had condemned Bush's warrentless wire tapping program.