I am constantly swapping my phones and find it's a pain to keep track of messaging, I will be in a conversation, then swap phones and lose track of that conversation for example. iMessage was pretty cool in that regard, although it only worked between iOS devices.
Is there anything similar to iMessage but that works in both iOS and Android?
There's an app for Android - can't recall its exact name at the moment (SMS Backup Pro, I think) - which can backup your SMS messages each night to Dropbox or some other cloud storage. Then, when you switch phones, you can restore your messages from Dropbox using the same app on the other device.
Requires a little bit of manual work (backups are automated, but restoring requires a few taps), but at least you don't need to rely on a third-party messaging service like WhatsApp or FB Messenger.
Edit: re-read your post. The app above is Android-only, so you can backup/restore from Android to Android, but not sure how to get it to work with iOS.