I'm just answering your question based on your "comment":
Fatwas are in first place a kind of Ijtihad of the scholar (mufti, sheikh etc.) that means he gives you an answer on your question based on the information you provide. Now in a one to one conversation he might have the opportunity to ask further question to get all relevant data or information, while on the net this generally isn't the case.
This can already be deduced from the Sahih hadith.
I am only a human being, and you people have disputes. May be some one amongst you can present his case in a more eloquent and convincing manner than the other, and I give my judgment in his favor according to what I hear. Beware! If ever I give (by error) somebody something of his brother's right then he should not take it as I have only, given him a piece of Fire."
(Sahih al-Bukhari, Al-Muwatta', and a shorter version in many other sources like Sahih Muslim and Sahih al-Bukhari)
Note: The quality of a fatwa may differ, as also the degree or level of wisdom of the person who is asking may differ. For example somebody who has more or less no knowledge about the rulings of Islam would be totally dependent on the given fatwa and he might be more interested on an explanation of the ruling than on a constructive explanation of the concluded fatwa itself. While a person with more knowledge would be more interested in proofs. In the following I would primarily explain my opinion on what makes a good fatwa for a learned person (somebody who knows at least a bit about Islam and is able to check literature) in the last part of my post I'll try to add a few words about a person who isn't in this position.
I won't say anything about a ranking of a fatwa as one couldn't give a ranking unless it's in the way I might describe. Let's say you've got an answer. If the answer was based on the Quran and you could clearly understand the meaning and how it was concluded, than there is not much doubt that this is "the answer". One could say the same about sahih Sunnah, but not that texts and what one could conclude is always a matter of Ijtihad and interpretation. So still even if the text doesn't clearly say so one could reject it as a "proof". So the more scholars of different schools approve this meaning the less doubt would be about it. As long as there is a kind of doubt or difference in interpretation one has a more or less free decision to make according common sense and use your mind and conscience, as once decided one is responsible for this decision.
Sometimes there's no text source in that case the way the ruling was extracted is important to check and follow as this would be Ijtihad via qiyas or any other "instrument" scholars use to declare a ruling, but it mostly will have a basis in Quran, Sunnah, Ijma' (if all scholars agree about that, and this would rarely be the case, many scholars declared something having Ijma' while it didn't have, maybe because the definition of Ijma' differs between sects or madhbas to some extent). IMO usually Ijma' is on something which already is affirmed by either Quran or Sunnah and maybe on a meaning extracted from weak ahadith.
So a good fatwa in first place is one where the mufti has clearly explained why or how he came to the conclusion (but this isn't always given unless you ask for it)! What you may do with this fatwa is your responsibility as a fatwa is not (always) binding unless it was pronounced by a Qadhi (judge) in a court in that case it is a ruling which may apply more or less immediately. A mufti in general has no legislative power, but can address the authorities (this depends on the kind of Question you asked about and the juridical implications). So if you disagree with a fatwa for good reasons (assuming it isn't a matter of juridical implications) you could seek a fatwa from an other scholar therefore fatwa is a matter of trust and also of authority (see also my answer here) and therefore it is not a common matter that a mufti explains exactly how he came to his conclusion, unless it is a written fatwa. But we are allowed to ask for proofs as Allah says:
..."Produce your proof, if you should be truthful." (2:111, 27:64) قُلْ هَاتُوا بُرْهَانَكُمْ إِن كُنتُمْ صَادِقِينَ ...
Read also the verses (21:24) and (28:75).
Of course a person who does not have the ability to check sources and don't know about the rulings of fiqh at all will totally be dependent on what the mufti says. Therefore such a person should look for a scholar he/she trusts in first place. This may mean a scholar of the same madhab -who in best case is able to explain his fatwa, so that the questioner can understand it well- of course one should ask for explanation and if possible ask other scholars too and use his conscience and common sense too.