The first app is the 'stock' e-mail app, and you can add any type of account in there. Is very feature rich, but not very customizable and some people just don't like how it looks.
The second app is the GMail app, which works best for GMail accounts if you want to take full advantage of GMail, but can also add POP3/IMAP accounts (like Yahoo, Outlook.com, Hotmail, etc.). For the GS6 in particular, however, you can't add Exchange accounts 'natively' to GMail, just to the stock e-mail app, and you can add them to GMail only if your server supports POP3 (not all do). If you have this kind of account, I'd suggest you stick to the stock e-mail for that one.