With commander, it does.
with the merchant, it does.
with the administrator, most action become much easier, farming overview form the captain also helps a TON.
Not a gold hater, but I'm just saiyan'
The effects of Commander are pretty much negated if the user of it does not have Phalanx, but their opponent does. It is also a relatively minimal bonus, in the grand scheme of things.
The Merchant does not directly give more resources as Osl said. It gives a minimal boost to the income from resource buildings which, as before, is pretty much negated by efficient resource management (upgrading resource buildings above your gold-using opponent), and regular farming (seeing as much of an active player's resources should come from farming, not resource buildings).
The Administrator does not automatically make things easier, it simply gives options to simplify how things are done. There are no significant bonuses - anything that can be done via the Administrator's overviews can also be done by a free player, it will simply take a little more effort.
The only thing I cannot argue for is the Captain's farming village overview which, as you said, helps a great deal. I think there is a proposal being voted upon currently that may make a version of that overview available for both free and premium players, though, so it is possible that that advantage too will soon be nullified.
The one other Premium option that I am against personally is the option to speed up construction/recruitment/research. Were I to have my way, that option would either be removed or limited far more severely. I think it was already mentioned that there is a limit of something like 5 times, but that is still far too much in my opinion. Even if it were limited to a single increase of 50%, that is a great advantage to a skilled player, who knows to fill his warehouse before adding troops to a queue.. combined with the spells of Poseidon and/or Hera, an even greater boost, while not allowing such ridiculous differences between free and premium players.