I recently purchased an iPhone 6. I neglected to remove data from my iPhone 5 before activating my new phone. Now it seems impossible to remove data from my old iPhone 5 as it is not active or connected to anything!
Make a backup of your old iPhone to iCloud, if you have wifi available, or iTunes, connecting your iPhone with a cable to your computer.
Then reset your new iPhone —provided there is no new information or data because resetting it will erase everything— and when asked choose "Restore from iCloud Backup" or "Restore from iTunes Backup", depending on the case. Chose the latest backup available, and you're set.
More detailed steps can be found here: https://support.apple.com/en-us/HT201269