There are two well-known disputes between HaRav Moshe Feinstein, zt"l, and HaRav Shlomo Zalman Auerbach, zt"l that demonstrate a point I think is important in understanding how halacha and the question-answer part of it is supposed to work.
The first case involves that of a shomer mitzvos doctor being on call at home on Shabbos and being called into the hospital for a pikuach nefesh case. According to RMF, not only is he allowed to drive himself to the hospital but after completing the case he can drive himself home even if it's still Shabbos. RMF's concern is that if the physician knows that he's going to be trapped at the hospital he will have a negative attitude towards involving himself in future such cases. In order to avoid this, he extends the heter of driving to the return journey.
RSZ has some problems with this. First of all, what kind of physician says "I could go to the hospital and save a life but it's such a bother getting stuck there so I won't"? If you're on call, you're on call! In addition, RSZ feels that a sense of professionalism would overcome any reluctance. Finally, he notes there are no precendents in halacha where a person is allowed to void a mitzvah because he was previously in a connected situation that allowed him to. Therefore he forbids the doctor from driving home after the patient's care is completed.
The second case involves trading call. If an observant physician is placed on call on Shabbos and tries to switch out, can he trade with a non-observant Jew? RMF says that he can because if the non-observant physician has the day off he will spend the entire time not observing Shabbos. While in the hospital, however, he will have an opportunity to participate in cases of pikuach nefesh so for those short times he will at least not be desecrating Shabbos. RSZ once again disagrees by noting that while the non-observant physician might be spending some time during the day while Shabbos is put on hold because of a life-threatening condition, he will not have the kavannah during that time that he is violating Shabbos at that moment because of the threat to life. For him it's just another shift on call.
Two things occur to me out of these two issues. The first is the absolute respect and regard poskim of the stature of RMF and RSZ had for each other. In the introduction to his teshuvah disagreeing with RMF regarding the driving issue, RSZ makes it very clear that he recognizes RMF's huge stature and even notes that he called RMF to ask permission to publish the teshuvah before going ahead with it. I wonder how much something like that happens today.
The second is the more substantive. What is the essential reason for the difference in opinion between RMF and RSZ? In the first case, one can suggest that the nature of the surrounding society is what led to the differing answers. In North America, a physician called to the hospital for a case of life-threatening illness faces a bleak time after the patient has been cared for. Let's face it, hospitals are not exciting places to hang around in unless you're actually working (and even then there are times...). It's even worse on Shabbos since one cannot simply go to the doctor's lounge and watch television or surf the internet. Other than endless pacing of the halls or dredging up some current journals, there is nothing to do. Then there's the companionship. In a gentile society, the Shabbos observant Jew is totally alone on Shabbos with no one around who understands the special meaning or environment of the day.
However, Israel's social setting is completely different. Most hospitals have shuls in which seforim can be found. If not there, within a block or two there will undoubtedly be a beis medrash of some kind. Other observant Jews will be at hand as well making such obligations as seudas shlishis less of a problem.
It would therefore seem that RMF paskened from the position of American society, recognizing the huge tirchah going to a hospital on Shabbos represented despite understanding the concept of professional responsibility. However, for RSZ these social issues simply did not exist and therefore his emphasis was on other issues.
In the second case, one can again look at the milieu each posek lived in and see how it influenced their views. In North America, the average non-observant Jew knows very little about Judaism, let along Shabbos. Yes, there is a small group of traditional folks that do know some things but the vast majority of our non-observant brethren know virtually nothing save that there's a problem with eating bacon and that Pesach means constipation after the seder. As a result, the average non-observant physician does not have either a positive or negative kavannah when it comes to activities on Shabbos. He simply doesn't have any kavannah because it never occurs to him that there is something special about the day that influences all his actions.
In Israel, the situation is quite different. Even though the educational system is not what it used to be, there is still a greater amount of Yiddishkeit that is transmitted in the school system. There is also the cultural difference. Chilonim are far more likely to interact with Chareidim and Dati Leumi folks than non-observant North American Jews with their local Orthodox. While 85% of Israeli Jews are not shomer mitzvos, studies show that the vast majority of them have a weekly Shabbos dinner and light candles for the occasion. The average Israeli Jews knows what Shabbos is. When he's working in the hospital he knows it isn't just another day and that there are folks out there who have strong opinions as to what is and isn't allowed before nightfall. Therefore he has a kavannah when it comes to what he's doing at any given time.
In both cases one can therefore suggest that RMF and RSZ came to different conclusions in their respective teshuvos based partly on the societies they lived in and their understand of local folk.
The point of this analysis is that all halacha is local. Nowadays many forget that. We get frequent pronouncements such as "Rav Eliashiv said X is forbidden" or "Rav Wosner says you're not allowed to do X" and the expectation that accompanies those pronouncements is that since a "gadol" said it, it's now the iron-clad halacha incumbent on all Jews everywhere, regardless of situation, circumstance or affiliation.
This, however, is a breach of the proper halachic process. The Chazal repeatedly note the uniqueness of every individual in terms of his relationship to Torah and the Ribono shel olam. Every person interacts in a way that is special and individual to him. A blanket psak violates this process by forcing a standard approach in place of the individual one.
This is the difference between "then" and "now. It is generally accepted that North American doctors follow the psak of RMF when it comes to driving home from the hospital and switching call with a non-observant physician. Israeli doctors, on the other hand, follow the psak of RSZ. Both are acting correctly because RMF's position is the halachic answer best suited for North America and the same is true for RSZ and his position. The modern alternative would be "Rabbi X says you can only do Y" and expect that physicians across the world accept a monolithic, one-tier answer.
Therefore it is important to remember that halacha is complex, that factors that might not even be obvious can play a huge role and that the only valid psak is the one that shows that the posek understands not only the shailoh but the shoel and his special individuality.