We filled ours out online, and it saved a lot of time in line at the terminal. We were on the Grand Princess, and if you had not filled out the paperwork online, you did not get Express Check-in. We went straight to our cabin check-in, and avoided the longer line where they had to check to make sure you filled out all of the paperwork correctly.
We had to fill out the Bahamas and SARS forms there, but that was quick.
I think the point is that there's absolutely no downside to doing it online if you can. Why wouldn't you? It's easy and fast and you save a stamp.
I believe that with most lines, the form is available as soon as your booking number is in the computer. You access the form using your booking number as your ID.
Always a good idea to print a copy of the form once you've filled it out and bring it with you in case the computer has a nervous breakdown on sailing day.
Some, if not all the lines have a cutoff a week or two before sailing for doing them online. Check the line's website.
It isn't that you get express registration so much as that all check-ins go faster when everybody's got their act together. That makes for an "express" experience all around. You show your passport, hand them your credit card authorization and they hand you your key. It's not much more complicated than that.
I filled my forms out online and when I got my documents for the trip all the forms were already filled in. I think that is where it helps. You still have to turn in the hard copy maybe. This is my first time and I haven't checked in yet.