I have my VCP5-DCV cert (5.5), and am now looking to get the VCP6-DCV. Is there an advantage of taking the Delta exam over the regular v6 exam? Is there different studying that should be done, or if should I be fine with the Delta exam if I feel I'm ready for the regular exam? Do I even have a choice of exams, or am I restricted to the Delta since I already have a VCP-DCV certification?
The difference between the full and the delta exam is actually the number of questions and the time you get to answer them. I'd expect more questions about new features in the delta exam. However, I can't tell you for sure, because I was in the same situation as you are now, and I chose to take the full exam.
Google helped me find these, which may help you:
To answer some your specific questions:
621D has fewer questions in less time.
I think you can take either 621 or 621D.
If you compare the objectives/topics of both exams, then yes if you're ready for 621 you should be ready for 621D.