Let's play this out a different way (Manning not in solitary). He's in a military prison, with military personnel. These are people who view what he did as ratting out his brothers in combat. He worked in an air-conditioned office, mind you, and hid behind the anonymity of the internet. He wouldn't last a week if he weren't in solitary. In that way, Manning's biggest problem isn't the government, it's the people he worked alongside.

Snowden is running away from having to take responsibility for his actions. It's not complicated. He knows full-well the penalties of revealing classified information, and acknowledged on multiple documents (going into his job) that he knew the procedures if he leaked any information. He leaked information. He doesn't want to go through that process, so he finds it easier to run to someone else in hopes that he won't face punishment.