Since importing my Evernote journal (2000+ entries) in to Day One I’ve seen a real slow-down in sync times. Switching from iPhone to iPad or vice versa will usually take around 3 to 6 minutes to sync the odd 3 or 4 missing entries using Dropbox sync, iCloud takes even longer.
The Day One team say they are working on a solution. Meanwhile this makes accessing Day One on more than one iOS device annoying if not unusable.