Is an ungrounded earth wire worse than no earth wire?
Yes, it's worse, in the sense that it is quite illegal in most jurisdictions.

A 3-hole outlet installed in a wall is a promise that the third pin is grounded. Suppose someone who doesn't know the truth plugs in a faulty piece of equipment and gets shocked because the ground is not there to protect them. You would be held liable for creating an installation that doesn't meet the building code.