After his attempt to have an affair via Craigslist was exposed, Chris Lee apologized and resigned. On the face of it, that was the honorable and right thing to do.
Anthony Weiner’s case is slightly different. Rather than using Craigslist in an attempt to have an affair, he used various means of communication (Twitter, phone, etc.) to send photos and engage in talk about sex. He alleges that he did not have an actual affair and had no intention of doing so. Since his credibility is rather low, it is not a matter of certitude that he did not have an actual affair or that he did not attempt to initiate one. However, his virtual affairs were morally unacceptable and his lying was certainly unethical.
As to whether he is worse or better than Lee is something of a tough call. While Lee intended to have an affair, he apparently did not succeed. Weiner, however, engaged in ongoing virtual affairs and then engaged in a prolonged campaign of deceit. I am inclined to say that Weiner is worse.
As far as whether a politician should resign after a sex scandal, much depends on the specifics of the case. However, some general comments can be made.
On one hand, if the actions are not illegal and do not violate the specific rules governing the office (such as congressional ethic), then the actions would not seem to warrant resignation. After all, what would justify expecting a person to resign would seem to require that it be actually relevant to the job. So, for example, if a congressman has an affair using his own resources, then he would not seem to have acted in a way that violated the conditions of his job. If a congressman used federal money to pay for his hookers, then that would be a rather different matter. On this view, Lee need not have resigned.
On the other hand, such a scandal can indicate that the politician’s moral character is deeply flawed in ways that render him (or her) untrustworthy. Unlike many jobs, a high level politician is expected to act in ethical ways and not grossly violate community standards. While this seems odd to say, politician’s depend on their reputation and a politician who has been involved in sex scandal often damages this asset to the point were they can no longer effectively function. While we will tolerate all sorts of sneaky dealings and we expect politicians to lie, the public is still very intolerant of sexual straying on the part of politicians. Bill Clinton is, however, an obvious example. As such, there is also the concern that such a politician will damage his party, thus also giving a practical reason to resign.
The worst part of the Weiner case is not the sexual aspect. That made him into a joke. The worst part is the campaign of lies. While we do expect deceit from politicians, that degree of unrelenting deception in this matter showed that Weiner is quite willing to lie in an unrelenting manner. It also shows that he has some rather weak reasoning skills-at least in certain areas. As such, it seems reasonable to question whether or not he is actually capable of representing the people of his district. There is also the question of whether or not they want him-which is something that must be decided by the due process of the next election. Since there are not any real competency requirements for most political offices, the confidence of the voters seems to be the only real test.