I set up my 6 as new.
I manually backup my photos/videos. I use iTunes match. I use google for contacts/calendars. So everything for normal use is synced via google or iTunes match. Many of my apps use iCloud for data (day one app, etc).
For game saves and other finicky app data, i use iexplorer and export/import. For example, every day photo app has 3 years of daily photos. I poked around with iexplorer and exported/imported my photo history into the new phone. Same for several games.
It took a little while, but I'm back like my old phone but with a fresh install.