Actually, there is no differential standard. The law doesn’t differentiate between who the mistreatment is being directed to. It’s irrelevant whether a black employee is harassing a white employee or vice versa. As far as I can tell, a lot of lawyers gave bad advice about this to their corporate clients over the last few years and the next few years are going to be embarrassing for them.
IANAL, but my understanding is that if you treat people differently based on one of the nine federally protected classes, you are in more trouble than if you treat people differently based on some other class (though treating people differently based upon a proxy for a protected class can also be an issue; e.g. redheads isn't a protected class, but it has correlations with both race and national origin).
Note that both of your examples given fall under the protected class of race/color. You still might have a more sympathetic judge and/or jury for one example or the other, so it might be relevant in practice, even if it is irrelevant by the letter of the law.
