Both, honestly.

It seems to me you're talking about the supermajority, not the filibuster - the supermajority was designed to do the things you name, but was only required in very specific situations. The filibuster on the other hand was not so much designed as improvised as a method for senators to stall or derail legislation they were very passionately against, back in the sixties with the civil rights for blacks. As has been pointed out a lot lately, the problem with the filibuster began when Senate rules were changed so as not to require actual talking and stalling in order to filibuster. Suddenly, it wasn't a measure of last resort that took heroic efforts, but something that took no effort at all and could be done whenever it was useful. The supermajority was always required to end filibusters, but it was the filibuster that changed and expanded, and so suddenly made a supermajority necessary in far more cases than was originally intended.

Well, you're right that both parties are guilty about the excess use of the filibuster, absolutely, it's not a partisan argument. It's a general argument about the state of American politics and the ability of the Senate to pass any kind of meaningful legislation - whether liberal or conservative.