Earlier quoted context omitted.
I know that different password storage schemes provide different security. I don't see how knowing what particular scheme they used would affect your actions.
If you use a secure password and the scheme the company uses is something like scrypt or bcrypt with high work factors, you can be near-certain that your password won't be cracked by an attacker. The amount of computation is just extraordinary. That said, you would still probably want to change your password if you're paranoid.
The same thing applies to knowing the particular password hash they used: if your password had enough entropy, attackers won't be able to break it even if eBay used "unsalted" SHA-1. But this doesn't change anything, because see previous paragraph.
If, say, your grandfather used the same password for Hotmail and eBay, and he tells you that his password was "bestjetpilot"[1], and asks for your advice on what to do, will you tell him to change both passwords, or just the eBay one? What if he used "y62BYmHoCsjScov6QSOgGCL"? What would you tell him? How would your advice change if you knew the particular password storage scheme eBay used? Do you now need to know which scheme Hotmail uses, because the password is reused on both websites?
[1] http://pages.ebay.com.au/help/account/create-password.html