When swapping out phones, I do everything the manual way.
Actually, I do this not just when swapping phones, but after doing a factory reset. Every time I download a new version of Android, my phone gets wiped, so this has become second nature to me.
Here's my procedure
1) Connect the old phone my my computer and mount it
2) Copy the photos out from the DCIM folder
3) Copy the Music out from the Music folder
4) I have ringtones that I created myself using Adobe Audition, and keep them in the Ringtones folder so I copy those
5) If there's any downloaded files I care about (attachments from emails, images from text messages) I check the downloads folder and copy them.
6) I have a folder that contains the APKs for apps that are not, or are no longer available on the Google Play Store, so I copy that.
I copy all of that to two places, a flash drive I keep at work and my NAS at home.
Plug in the new phone, or freshly wiped phone into my PC, and just copy all of the data back over. Takes only a handful of minutes.
A few years ago I took a few hours and I created a fairly extensive contact list in Google Contacts and since then have made an effort to keep it up to date and correct, so I never have to worry about that again.
I'm generally not concerned about keeping text messages, in fact, I'd delete them myself usually every couple weeks. I only send/receive about 10 text messages a week so it's not a big deal.
I like having to re-download all of my apps again. It gives me a chance to keep off the crap I thought I'd use but end up never using. In the Google Play store, under the My Apps & Games section, there's a tab called Library that lists every app you've ever downloaded using the Google account you're signed in with. When I re-install apps, after all of the system apps are done updating, I go there, and just tap on Install for all of the apps I want to redownload.
Then comes the fun part, after all of the data is loaded after all of the apps are downloaded. The customization of the phone.
I don't know about you, but my phone's settings are heavily customized and I use a third party launcher. I use the US AZERTY keyboard with a black theme, custom Lock screen message, allow the side loading of apps, hide notifications from the lock screen, make text size small, enable the System UI Tuner, turn off auto brightness and a bunch of other stuff. After that is complete, Nova Launcher gets set up, and customized to my liking, and then comes the process of setting up my home screens the way I like them with widgets and icon placement.
