I am at the point in my life that the time invested in following our teams is a substantial sacrifice, and to that end, I would almost prefer that a team be categorically bad just so I could quit caring so much and take the "ignorance is bliss" approach of a more casual fan (i.e., no "appointment viewing" of games, not caring if I miss a game or two or three or more, and even instances of checking the outcome before making the decision of whether I want to watch a game or just delete it and move on - a hallmark of the later Groce and Beckman eras...) The constant agony, time commitment, and general overall disappointment of the two scenarios you describe are in some ways much worse than just sucking so bad it's impossible to care, though I certainly realize and appreciate that others will feel differently.
But I'd say that the first scenario is worse because there's presumably less basis to hope for improvement.