There's an update out today for DEVONthink To Go that dramatically improves document syncing. DTTG will now sync in the background after a new document is created. Sync will continue as long as the device does not lock. If the device does lock, it provides a nice notification on the lock screen to reopen the app to continue syncing.
It's nice to see this gap closed. DEVONthink is a tremendous out-board brain for me but capture can be a bit tedious on iOS. Background sync helps a lot.