Well you can do it a few different ways. However none are a 'direct' transfer.
You can try uploading all the files (photos, etc.) to your google account from the older phone and then download them onto the new device.
You can also email them to yourself from the one phone and then download them from the individual emails on the new device.
There is the option to move all the files from the phone itself over to an SD card and then transfer the SD card from that phone to the other phone.
Or, which is the quickest way, you can connect the old phone to a computer via USB cord and copy or move all the files you want from the phone to a folder on the computer. Once done, disconnect that phone from the computer and connect the new phone...