Actually the opposite is true.

By joining the EU they have voting power and influence over their own destiny which they lack under those agreements. Currently they must accept EU rules without being able to influence them.

> they must accept EU rules without being able to influence them

No, they don't really must accept all rules. Only the ones that will benefit them. This will cease once they join the EU.

You might be confusing this with the Switzerland situation. The EEA states (Norway, Lichtenstein, and Iceland) indeed must take all legislation that’s part of the EEA into their domestic law. Sometimes directives and regulations have cave outs for countries but they’re rare.

Implementation is overseen by the EFTA Surveillance Authority who can sue members in the EFTA court.

They have negotiated exceptions, but they can also do that as EU members.

Influence on the rules that they are practically forced to follow. Like Norway Iceland has plenty of agreements with the EU, but that translate to copying EU regulations as if they where an EU country already, except they have no say in the making of those rules.