Ok, there seems to be quite a bit of confusion here that I hope I'll be able to clear up:

First of all, the intentionalist-functionalist (IF for the purpose of this post) debate is not about about the responsibility or reasons for the rise of the Nazi party or the creation of the Third Reich. While it does have some implications for these questions, the IF debate is foremost about what factors lead to the Holocaust.

Intentionalists posit that the physical destruction of Europe's Jews had been part of the Nazis and specifically Hitler's political program ever since the early 1920s. They explain the genocidal actions of the Nazis through a long held political program – their intention.

Functionalists or structuralists do not dispute that the Nazis had a long standing anti-Semitic political program. What they posit is that mass-murder on a grand scale had not been part of that program from the beginning. Rather, their position is that influenced by factors such as the political structure of Nazi Germany and the dynamic between center and periphery as well as the ideological dynamic, the Nazis gradually radicalized towards a position in which the murder of all of Europe's Jews seemed to them like a viable political solution.

I have previously discussed this debate in our podcast, here discussing Hans Mommsen's functionalist theories, here, discussing the evidence of the Intentionalist side and here discussing its current day impact.

While I am happy to go deeper into the exact debates and there evidence if you have questions about that, I think another really important point is that this discussion can be considered resolved and over. New research and analysis has lead to to a scholarly consensus on the question that is influenced by both positions but leans more into a functionalist direction.

As I write in one of the answers linked above, the prevailing interpretation today is that of Ian Kershaw who thinks the functioning of the Third Reich in terms of "working towards the Führer". Kershaw relies on the model of the Third Reich, that relies upon Hitler in his role as the Führer as the center actors within its structure tend to gravitate towards and who do not need a direct order.

The political structure of the Third Reich must be imagined as one of competing agencies. Essentially agencies and institutions were given the same task within the Third Reich and thereby put in competition on who was able to do it better in the eyes of the Führer. Doing in better in the eyes of Hitler was a huge political asset in this structure because it meant that you or your agency would receive further political power and responsibility. Thus, the field of politics became a battleground between various agencies and institutions all trying to anticipate what Hitler wanted; they started "working toward the Führer" in the words of Kershaw.

It is also important to note that the IF debate is in essence a very German debate that has been resolved in part through the political and historical changes in Germany and the generational change among historians. Intentionalists were on the whole older German historians who followed a model of history that tends to emphasize politically important individual historical actors. Furthermore, many of them were socialized in a political climate that tended to locate responsibility for the crimes the Nazis committed first and foremost in the person of Adolf Hilter. Younger German historians, many of them functionlists, instead were interested in a different approach to history, one that explores it through looking at structures and dynamics. Also, as people born later, they were less inclined to blame Hitler for all the bad that happened and in terms of responsibility cast a wider net.

In that sense, the debate was not only about historical facts about the Holocaust but also about Germany, its dealing with its past and historical responsibility of the German people. With yet another generational shift having occurred, these debates lost their urgency and the interest of younger German historians. With the decided shift in tone in Germany's dealings with its past throughout the 80s, German historical responsibility for the crimes of the Nazis lost its contentiousness in the broadest sense and thus, younger historians had not qualms about moving beyond the IF debate or incorporating factors form both sides.

This is also one of the reasons, for what /u/kieslowskifan describes in one of the linked threads: Namely, that the debate had very little impact on US and generally anglophone academia that dealt with the Holocaust.

With all that said, it is further important to note that neither Shirer nor Evans were part of this debate. Shirer, while he would probably use some of the arguments made by intentionalists, is not a historian, too early for the debate and does not belong within the matrix of this debate altogether. Evans on the other hand is much later than the debate and has in his works moved largely beyond the points that were raised in the debate as contentious.

The point is that while the question of political structure and historical focus that were raised in the IF debate does indeed play into answering the question who was responsible for the rise of the Nazis, it was not the focal point of the debate and a variety of historians on the two sides of the debates would answer that with a variety of answers.

I can go into what for example Mommsen and Broszat as functionalists say about this questions vs. what for example Karl-Dietrich Bracher, an intentionalist would say but for now, I'll stick to the two you mentioned, Shirer vs. Evans.

Shirer, having written his book in 1960 is strongly influenced by theories about Nazism that predate the IF debate, namely the German Sonderweg thesis. The Sonderweg thesis has a history that goes back to WWI but it gained some traction after WWII and is strongly linked to the Fischer controversy about Germany's responsibility for WWI. In essence, the Sonderweg thesis posits that Germany is not like the other nations in Europe, that it followed a special path (a Sonderweg). Germany's late reunification and its very unique culture of being a nation that is to almost equal parts Lutheran and Catholic as well as several other factors lead certain historians and Shirer to conclude that there was a straight historical line to draw from Luther to Hitler, where national socialism was the unique product of a unique national history. Because it ignores the impact of modernity and thinks in categories like the "correct" way to become a nation state from which Germany was allegedly an aberration, the Sonderweg thesis is largely discredited today but if you ask Shirer what was responsible for the rise of the Nazis, he'd answer, German history and culture back to Luuther made the Germans more authoritarian and anti-Semitic than other Europeans.

Evans on the other hand delievers a much more nuanced and credible answer to this question in the sense that while racialist nationalist discourses from Germany of the 19th century did indeed play a role in the rise of the Nazis in Germany, there are a whole slew of historical factors to consider including but not limited to the loss of WWI, the political culture of Weimar, the economic crisis of 1929, and the attitude towards Communism in Germany mixed with the experiences of attempted revolution in 1919 etc.

As with the question how the plan for the murder of all Jews originated, the question about who or what was responsible for the rise of the Nazis is incredibly hard to pin down to snappy answer. Like any historical question, it is possible to identify factors and weigh their importance but a penultimate answers escapes the historian for like in contemporary society there often is no one causal reason for social and political developments.

Sources:

• Richard Bessel, "Functionalists vs. Intentionalists: The Debate Twenty Years on or Whatever Happened to Functionalism and Intentionalism?" German Studies Review 26, no. 1 (2003).

• Christopher Browning: Fateful Months : Essays on the Emergence of the Final Solution, New York : Holmes & Meier, 1985.

• Christopher Browning: The Path to Genocide : Essays on launching the Final Solution, Cambridge : Cambridge University Press, 1998.

• Christopher Browning: The Origins of the Final Solution : The Evolution of Nazi Jewish Policy, September 1939 – March 1942 (With contributions by Jürgen Matthäus), Lincoln : University of Nebraska Press, 2004.

• Richard Evans' Third Reich Trilogy.

• Ian Kershaw: The 'Hitler Myth'. Image and Reality in the Third Reich (Oxford, 1987, rev. 2001).

• Ian Kershaw: "Working Towards the Führer: Reflections on the Nature of the Hitler Dictatorship" pages 103–118 from Contemporary European History, Volume 2, Issue #2, 1993; reprinted on pages 231–252 from The Third Reich edited by Christian Leitz, London: Blackwell, 1999.

• Ian Kershaw: The Nazi Dictatorship. Problems and Perspectives of Interpretation, (London, 1985, 4th ed., 2000)

• Ian Kershaw: Hitler, Vol. 1 and 2 (rev. London 2008).