Specifically, what rights does a non-EU member in the EEC not have? And what restrictions can it avoid being out of the EU but in the EEC?
What it would gain: A direct influence on EU policy (concretely that means a seat at the Council and a permanent representative but also a Commissioner, judges at the EU courts, EU civil servants, etc.) that it must implement anyway. Right now, Norway is effectively a rule taker.
What it would lose: Independent fisheries policy. There would probably be a few other adjustments, maybe some budget contributions and of course an apparent loss of sovereignty but the main thing is clearly the fisheries.