Groupme is using SMS only if you're an outsider to the group and you send an SMS to the group's phone number. GroupMe is basically a mix of SMS and IM for groups. The SMS is for groups, and the DM's are for 1on1.
If you're using GroupMe to send pictures to another single phone, that's fine since its using data in that case, but if you want something that is more robust and data-only, I would suggest Whatsapp as a true iMessage replacement.
Imo is great as well, but it's basically an IM client like Adium or Pidgin for Desktop.
If you want something you never have to log in to or get an account for, Whatsapp is the best thing for all smartphones right now. It's the iMessage of all smartphones, basically.