Ther is no doubt that the greatest warship was Prinz Eugen. The amount of conflicts that ship went through and only came out with minor damage was astonishing. It even sailed through the English channel with Scharnhorst and came out with a few minor hits nothing that couldn't be repaired quickly. Even after the war it survived as a training ship for many years to the US Navy.
No doubt that Prinz Eugen was the greates ever warship.
I agree that PE was a great ship, one of the greatest ships ever. She even survived a nuclear blast without sinking.
But the reasons you quote for being the greatest betray her in favor of another ship that saw a lot of more action: HMS Warspite. A WWI veteran that fought in Jutland, did all her service during the "inter war" years, fought in almost every scenario of WWII and still have the distintion of firing the longest shot (that hit, that is) ever against the Italians. In that order of things we must recognize Warspite.
But I´ll recognize Bismarck and Hood as the two greatest ever.