Chapter 12 of Vol III of the MSM lays it out pretty clear (as clear as the government can be).
To summarize, a 3A/E will also get you a DDE limited which you may be able to upgrade to DDE unlimited with 6 months sea time. When you upgrade to 2A/E unlimited, you can also get a Chief(limited) Oceans, Chief UFIV and DDE unlimited.
Interestingly, it says that as a 3A/E you cannot serve as a DDE limited without the endorsement even though you can get the DDE endorsement when you get your 3A/E.
I wish I knew all this when I renewed my 3A/E last month.