As a man, you could be charged with rape in either of the two scenarios. It really depends upon the law of the land, which is something that would be a really good thing to know if you think you may find yourself in either scenario. Really good as in your freedom/life may depend upon your knowledge of such governing laws. 

The first scenario would be easier to prosecute in court. 

The second one could still end the same way. In a just system, you would both be charged with raping each other because neither was capable of giving consent according to the State, but in reality, women are virtually always the only ones incapable of giving consent when intoxicated. 

Here's the thing: if the woman in either scenario has no reason to file charges against you, it's not going to court. There are no Rape Police who jump in through your window, post coitus to adminster breathalizer tests to see if either or both persons are over the limit for intoxication.

Simple enough?

I'm sure there have been more than just a few long term relationships that started out with exactly the aforementioned scenarios. 

if women just stayed inside there would be no chance of getting raped (by non-family members) /sarcasm

I hope not, otherwise I'm a victim quite a few times over.

In short no.

If one is drunk beyond sense and the other is sober, potentially. I think it should only count as rape if the drunk individual doesn't ir cannot explicitly express consent/interest but simply complies (doesn't reject) the advances of the sober one. If they are conscious and actively reciprocate or even pursue the sober one then I don't think that should count as rape. I wouldnt mind a more minor misdemeanor existing to encourage people look after each other and act responsibly in those situations though.

If both are drunk beyond sense and both consent in their drunkeness then no, it shouldn't count as rape and they are mutually at fault if they regret it.

Unless drugged I really don't think we should encourage people to negate the responsibility they have to look after their own judgement. If you invite someone into your house when you're drunk, can they be arrested for home invasion? Or if you give something away in your drunkness, can you then accuse the recipient of theft?

Pretty much this.

As a guy, you could be on the verge of alcohol poisoning, and a stone sober woman could take advantage of you to whatever end and get away with it.

A woman, on the other hand, could have a BAC of .00000000000000001 (she sniffed a shot or something) and it will be rape if a guy so much as gets to 1st base with her.

My advice is to be hyper vigilant when drinking with a girl you don't know. Maybe ask some probing questions about where she stands on consent, feminism, etc. Even then I wouldn't trust her...

Depends on how drunk the person is, but I question why the OP doesn't include a scenario where the male is the drunk party. Power structures etc?

No it isn´t if you consider that rape than 90% of the people who has ever had a one night stand is a rapist. If the girl or the guy regrets it afterwards it´s a form of selfmutilation, which isn´t a crime besides the person agreed with it at that time. As others said if you can´t make reasonable decisions while you are drunk, than don´t get drunk. You can´t expect society to act responsible if you yourself aren´t able to do that because you are to freaking drunk to think logical.

Statistically speaking, the majority of rape that does occur is by someone the victim knows. It is actually rare for an individual to be raped by a complete stranger. At least know what you are talking about, before making a baseless suggestion. Hey, it is the internet, where everyone has an opinion, regardless of how much they actually know about the topic. Also, the person who is raping you can lure you away from your good friends (friends can get seperated). If you are lacking your basic cognitive skills and someone takes advantage of that, they are definitely in the wrong.

@OP. The first scenario is definitely rape. The same rule applies for sales. Legally, you cannot make a point of sale to someone who is intoxicated, as this is taking advantage of that particular individual.

Just because you are intoxicated, does not mean you are asking for trouble to happen. Some people become intoxicated unintentionally, as the degree in which you can handle alcohol can actually very depending on your mood, health etc. 
Even if you intended to get intoxicated, as you might be celebrating a promotion, graduation etc. does not mean someone should take advantage of you.

You're forgetting that is some (all?) common law countries, rape literally cannot be comitted by a woman, so... no, it's only you who raped her.

Agreed. But... is consensual sex "taking advantage" of someone? Unless you see sex as a one-way transaction, I would argue that it's not.