I have embraced GPS technology for other activities including trail running, hiking, and sailing, but have never warmed up to it that much for bike touring. I find their battery hungry nature to be more hassle than they are worth. I do have a smart phone as a backup, but leave it turned off except when using it. BTW, it seems to get a fix in 1-2 minutes on the rare occasions that I use the GPS.
I go with paper maps, but once in a while do use my phone to find services or local directions in town. If on an AC route I like their maps but since I tend to deviate from their route I usually pick up state maps as I go. I either give them away, discard them, or mail them home when I leave a state. If I have trouble finding a state map I am likely to use the phone's GPS more.