Quote - "As it stands, in the US, you need to register a work before you can sue."

My understanding is a little different.  You can sue in either case, it is what you can sue for that is different.

If it is registered, you can sue for damages.  If it is not registered, you can only sue to stop distribution/publication/sales of existing copies, but no monitary damages.

Close, but not quite right.

You cannot bring a suit in a US court for copyright infringement unless the copyright has been registered with the US Copyright Office. Period, end of sentence, full stop. The court will throw out your suit. (Although "without prejudice," which means you can register the copyright, and then refile your suit.) Fun fact: I once had a client who was sued in state court for breach of contract. The court ruled that what the plaintiff was really suing for was copyright infringement and threw out his suit because state courts don't have any jurisdiction over copyright infringement. He moved to a Federal court. The Feds asked him if he had the copyright registration. He said, "No, and I can't get it due to StMarc's client's dastardly doings." The court said, "That's a shame, Mr. Plaintiff. Case dismissed."

Edited to Add: Moriador is quite correct that the question of whether a copyright created in another country, and otherwise in compliance with that country's laws, is required to be registrered in the US before suit for an act of infringement that took place in the US is not definititvely settled. It won't be until the SCOTUS rules on the question, if it ever does. But, and this is not legal advice, in my opinion the general rule should be that a wise person will register before filing suit, even for a Berne/Paris-style copyright. There is a procedure to expedite the issuance of  the certificate if you are in need of it to file a suit against an infringer.

*Also, Moriador wonders about whether somebody could file a copyright application on someone else's art, effectively "stealing" the copyright. Yes, they can, it happens all the time. We have procedures for dealing with it which are outside the scope of this post. It is essentially what the plaintiff alleged happened in the case I referred to above. The court didn't buy his argument.

The distinction you make is a real one, but it doesn't do what you think it does. You can always sue for an injunction to stop the infringer doing what they're doing, and you can always sue for actual damages. What it controls is whether you can sue for statutory damages. These damages are set by law and form a minimum level of damages which do not depend on the actual damages (lost revenue, profits, etc) suffered by you. It can also control whether you are eligible for damage multipliers: wilfully infringing a registered copyright can lead to awards of up to TRIPLE damages plus costs and fees, which is a LOT of money. Minimum statutory damages are $750 per work, and maximum is $150,000.