x2 on what MisterMe said.
Check your Mail accounts on both OS X and iOS -- I'm betting you'll see that they're using the POP protocol. The POP protocol doesn't allow for keeping email in sync between multiple devices. No email program can fix that.
If your accounts are set to use POP, then check to see if your email provider supports IMAP. IMAP (and Exchange) protocols allow for keeping email in sync between multiple devices. Unfortunately, not every email provider supports it.