Wow, that doesn't sound right (unless the videos were huge). You can upload the pictures and video to a cloud service like Google Photos and share from there; that would be the easiest way to do it and the fastest since you can use WiFi for it.
If you don't want to go through a 3rd party, then you can share the content directly, phone-to-phone, via WiFi-Direct through the SHARE menu (select the media you want to share on the Gallery, tap the menu button, select SHARE). That will create a direct link on your phones but use WiFi instead of Bluetooth to transfer the files (you don't need a router or to be on the same WiFi network, this happens phone to phone).
BTW, NFC doesn't really transfer anything, it just acts as a 'handshake' and then hands over the task of transferring data to, usually, Bluetooth.