Originally, I thought I'd call, but then I ended up doing it online and am very glad I did. Doing it online allows you to be more self-sufficient in that YOU can easily alter the request time if necessary, YOU can see the alternatives coming up.
I had heard that sometimes if you can't get something online, you can get it if you call. I ended up trying that (in my case, getting an earlier 50s PT ADR) and while the CM was very nice and very helpful, I found it to be a painful experience. It seemed to take soooo long and I didn't get the earlier ADR anyway. But even telling her the number and ages of my party members seemed to take a long time to get into the system.
Comparing the two, I personally found online just a much more efficient way to book.