There is a great difference in degree. First, Clinton had a long history of womanizing, which he would not admit too. This made him vulnerable to blackmail. This was a very reasonable concern, considering the fact that he lied under oath to cover it up. Secondly, his womanizing was ongoing. Third, he was plausibly accused of rape.
Newt's first marriage began as a relationship between a teacher and a sixteen-year-old boy (Newt). Catholics could consider this marriage null, because of a lack of consent. The failure of his second marriage does not appear to be excusable. But even here, the marriage would be null, because this wife was previously married, and not free to remarry. Still, this doesn't justify his initial relationship with Callista.
Newt and Clinton's behavior patterns are significantly different, but I don't expect Newt's opponents to analyze his behavior objectively.
I havent substantiated this for myself, but my understanding from a post I read earlier today, that the 2nd ex was trying to peddle influence. If that is true, Newt had very good reasons for saying goodbye.