Complete breakdown of account level features. The highlights:
Free accounts get 2 character slots per nation (per server, I think). Since they consolidated servers way back, you can play one nation per map cycle, switching from one cycle to the next if you wish. Premium and Captain's Club accounts get 6. Free accounts may purchase more as microtransactions.
Verdict: Not really gimped at all, especially since economic plots are per account.
Free accounts get 2 dockyard slots per character. This means you can have two ships at a time, and transfer between their two locations if you sail them to different places. Premium and Captain's club accounts get 5. Free accounts may purchase more as microtransactions.
Verdict: hardly gimped. 2 is a bit tight, but that's still enough to have a cargo hauler and a combat ship if you like. Red zones will pose more of a threat, though, because if the port you're docked at with your 1 combat ship is flipped while you're offline, you don't have the easy out of transporting to another combat ship and playing normally from there. Instead, you'll have to sail out through the PvP area.
Free accounts don't get ship storage slots. I'm not exactly sure what these are -- I think they may have added a feature where you can stick an old ship into storage instead of using up an active dockyard slot for it. Premium and Captain's Club members get 100 per character.
Verdict: I can't recall ever using it, whatever it is, so it probably isn't a hassle. Can be purchased as microtransactions, regardless.
Free accounts get 2 economic plots account. Premium and Captain's Club get the full 10. Free accounts can purchase more as microtransactions.
Verdict: A bit of a handicap. It'll reduce the amount of money you can make "crafting." That said, if you're not heavy into PvP, 2 plots (or purchasing a few more; these would probably be my first or second recommendation for taking advantage of the microtransactions, along with dockyard slots) along with normal PvE action ought to be able to keep you relatively comfortable as far as being able to afford ships. If you plan on PvPing, you'll want the extra cash flow afforded by running a more comprehensive economic venture.
Free accounts don't get ship insurance (reimburses you some money when your ship sinks). Premium and Captain's Club accounts continue to get insured for free. Free accounts can insure their ships as a microtransaction, looks like.
Verdict: minor nuisance. The game released without insurance, and the payout doesn't replace a ship at market value anyways, and is often quite small.
Free and Premium accounts must purchase access to "Premium Missions." These are the multi-group PvE missions at the high end, and perhaps the daily cash missions for max levels, too.
Verdict: Do you like raiding? From what I hear, the loot is nice, but in that self-perpetuating raid to raid better stuff way. Probably pretty necessary to get the edge in PvP, too. I'm not sure how much content has been added since I stopped playing, so I don't know how cost-effective it would be to just buy the missions.
All in all? Free is a good bargain to get your feet wet and level up. Paying for a month and cancelling is a downright steal. Ongoing subscriptions are really only worthwhile for heavy PvPers, alt-o-holics, and maybe raiders.