Its power derives from persuasive ability and moral authority. For the President to be censured would be to rob him of part of the requisite authority for him to function, while leaving him responsible for the duties of office. Censure keeps the President in office, while hobbling his power. Impeachment by the House of Representatives is certainly implied censure, but Senate acquittal serves to renew and revalidate Presidential authority. After impeachment by the House, the Senate options are either to convict or acquit.
Censure is problematic in another sense.
There are two reasons that Senators could have opted to acquit in Clinton's case. The first is that they could have found, erroneously in my opinion, but nonetheless found, that there was insufficient evidence to convict of perjury, obstruction of justice or any other public matter. If the evidence is not sufficient, censure is not appropriate. Censure, under this circumstance, would appear to punish Clinton for private lewdness, not public sins. The second possibility is that Senators are persuaded of his guilt, but chose to excuse perjury and obstruction of justice because it is politically expedient.