If both your devices are on the same local network, start with Bonjour-based synch. I and many others find it very reliable and fastest method. All explained in the outstanding DEVONthink Handbook, with elaboration at Bonjour Simplified
You can continue to setup and use Dropbox also and you can use multiple sync services, but don’t go overboard. That will support you when the devices are not on the local network, if that important to you.
Also don’t sync “too much”. Not only are IOS devices limited in space, but syncing simply takes time to finish, esp. the first time. Ensure you are giving Dropbox and DEVONthink time to finish.
Only sync those things you really need to be synced. For me, I focus on synching stuff that I want to read or stuff that I know I will need to refer to. I don’t sync stuff “just in case I want” to see that electric bill from 2019.
I use Dropbox all the time and it “just works”.
Re nomenclature, you use the word “delete” everything, but the term you should be looking for in DEVONthink is “clean” to remove the sync folder on Dropbox.