Sorry for the late reply Lady B. Soo much has happened since I was gone - I had hard time finding the entry where I left off
I'll try to answer your questions regarding Sahih(meaning authentic) Hadith. However, I would add a disclaimer that I am no scholar of Islam, just a layman.
Let me first clarify one thing - it is not about who's more reliable Abu Bakr or Ayesha(may Allah be pleased with them both) at all. All of the well known companions of the Prophet(pbuh) are trustworthy and reliable. However, neither of them came to me or you directly and told us that Prophet Muhammad(pbuh) said this or that, right ? So the reliability issue is on the people who informed us about what they said about Prophet Muhammad(pbuh). Let me give a bit more detail.
"A hadith is a saying of Muhammad or a report about something he did. Over time, during the first few centuries of Islam, it became obvious that many so-called hadith were in fact spurious sayings that had been fabricated for various motives, at best to encourage believers to act righteously and at worse to corrupt believers' understanding of Islam and to lead them astray.
...
While the early collections of hadith often contained hadith that were of questionable origin, gradually collections of authenticated hadith called sahih (lit. true, correct) were compiled. Such collections were made possible by the development of the science of hadith criticism, a science at the basis of which was a critical analysis of the chain of (oral) transmission (isnad) of the hadith going all the way back to Muhammad.The two most highly respected collections of hadith are the authenticated collections the
Sahih Bukhari and Sahih Muslim. (Sahih literally means "correct, true, valid, or sound.") In addition to these, four other collections came to be well-respected, although not to the degree of Bukhari and Muslim's sahih collections. These four other collections are the
Sunan of Tirmidhi, Nasa'i, Ibn Majah, and Abu Da'ud." [1]
So normally if you rely on Sahih Bukhari and Sahih Muslim, it should be authentic. However, you have to remember that, for example, Imam Bukhari collected more than 100,000 hadiths and then kept only 7000+ in his Sahih collections out of which only 20 or so some Islamic scholars say are questionable. But they don't just say it is questionable out of the whim - they only do so if they didn't agree with the authenticity of the chain of narration of the Hadith listed in Bukhari.
Here's a glimpse of what is involved in deciding if a Hadith is authentic or not:
*Unbroken chain of narrators going all the way back to Prophet Muhammad(pbuh)
* "Each reporter should be trustworthy in his religion; he should be known to be truthful in his narrating,"[2]. For example, if X said he heard/got the narration from Y and it was found out that they were not contemporary and could have never met - this narrator won't be considered trustworthy.
* "to understand what he narrates, to know how a different expression can alter the meaning, and report the wording of the hadith verbatim, not only its meaning. This is because if he does not know how a different expression can change the whole meaning, he will not know if he has changed what is lawful into what is prohibited."[2]
* "Moreover, he should be a good memoriser if he happens to report from his memory, or a good preserver of his writings if he happens to report from them." [2]
So as you can see there's a lot involved in determining if a Hadith is Sahih or not. Another basic rule for checking authenticity is that hadith should not contradict what is said in the Qur'an.
Just a side note : often times people who want to attack Islam would quote stuff from known fabricated Hadiths, or quote partial Hadiths, or quote weak Hadiths(with broken chain or unreliable narrators in the chain), or quote from some sources which were written before Bukhari or Muslim went through the science of verifying the chain of narrators to discard the unauthentic ones.
Hope this helps.
References:
[1]http://islam.uga.edu/hadith.html
[2]http://www.islamic-awareness.org/Hadith/Ulum/asb7.html