Speer's sentence of 20 years imprisonment was lenient when compared to the others he was tried with at Nuremberg primarily due to his cooperation as well as his straightforwardness with his captors immediately after the war and during his trial. It was also likely due to the fact that Speer arguably only attached himself to Hitler and the Nazi cause to further his career as an architect (though that does not excuse his close association with Hitler and the Nazi Govt.) and that he was not as much of a devoted Nazi like many of his co-defendants, whereas Hess had been a devoted member of the Nazi party since 1920.

First off, when he was initially captured, Speer assisted his captors by providing them with first hand information on how effective the strategic bombing campaign had been against Germany and it's war industry (Speer was Minister of Armaments from 1942 until the fall of the Reich, so he had a very useful insight into just how effective the air campaign was against Germany). Keep in mind that Speer's cooperation with the Allies in the post-war occupation was far more cooperative and beneficial than what many other former high level Reich officials were willing to offer their captors in the months immediately following the wars end.

Another reason as to why his sentence was so light when compared to many other high level Nazi officials was that he accepted responsibility for actions taken by the Nazi regime without trying to use the "Just following orders" or "I did not know about any atrocities" arguments to remove some of the blame/responsibility from himself. While Speer definitely oversaw some areas of the Third Reich that had atrocities attributed to it (slave labor being used within the armaments industry for example), Speer accepted responsibility for those atrocities that occurred under his ministry and others that his office had no oversight/control over. Speer made a statement during his [cross-examination] (http://law2.umkc.edu/faculty/projects/ftrials/nuremberg/speer.html) that explained that he believed that any high official within any government bears two responsibilities. One is to whatever area that high official is tasked to administer and the other, is the common responsibility for all State actions, shared by all high level members of a government, regardless if their ministry or office doesn't have any direct involvement or knowledge of those actions.

This is one of the key reasons why it is likely that Speer's sentence wasn't as harsh as it was for Hess or other surviving high-ranking members of the Third Reich. This defense however, is still deemed controversial today, as it gave many holocaust deniers a convenient way to try paint Hitler as unaware of the activities carried out by Himmler and the SS against the Jews and other persecuted groups during the war (which, to be nonacademic for a moment, is a bullshit excuse).

Speer also claimed he had contemplated killing Hitler as the war took a turn for the worse for the Germans in order to save the German people from total destruction. However, most historians, as well as both Allied and former Reich officials participating in the Nuremberg Trials, doubted Speer's plans were anything more than an attempt to make him appear more sympathetic to the Judges at Nuremberg.

In the end, Speer was given a 20 year sentence (and this was not something that was unanimously agreed upon by the eight judges of the trial, there were two days of discussions before his sentence was decided upon), despite three of the eight judges originally calling for the death penalty to be sentenced.

Hess was given a harsher sentence compared to Speer for a couple of reasons. The first of which, is that he was not nearly as cooperative as Speer had been. Though Hess had been captured early on in the war after his unauthorized flight (which some claim Hitler had secretly authorized in hopes of enticing Britain to make peace and ally itself with Germany against Stalin once that war began) to Scotland in which he tried to broker a peace treaty and possible anti-soviet pact between the British and Germany, all accounts point to him remaining a committed Nazi throughout the war while in captivity and refusing to cooperate beyond asking for a negotiated peace treaty.

Hess also did not attempt to accept any of the responsibility of the Third Reich's actions on the same level that Speer had during his testimony and defense. Hess's defense argued that because he had not been an active member of the Nazi Regime since May 1941, he could not be held responsible for War Crimes committed by the Third Reich after that date. They also argued that the charges laid against him for preparing and planning a war of aggression (primarily due to his signing of multiple government decrees such as the Nuremberg Racial Laws and mandatory military service) were invalid since those actions (despite Hess's admission of responsibility for them) were committed internally by a sovereign state official and were beyond the jurisdiction of a war crimes tribunal.

The judges did not agree that his responsibility was beyond the purview of the court, and he was given a life sentence after being found guilty for his involvement in planning and preparing a war of aggression. He was however, found not guilty of crimes against humanity and war crimes carried out by the Nazi Regime (the majority of those charges stemmed from events occurring after the start of the war between Germany and the Soviet Union).

I should also mention that Speer did make himself available to many historians after his release and that he went on to author two books about his experiences as a high level official within the Nazi Party that are still widely used by historians, though with some caution. Richard Evans uses Speer's writing quite a bit in his works (specifically the Third Reich Trilogy ), though he is quick to point out that one must be careful in using them as Speer is more a less, an unreliable narrator of his own actions and awareness during his time as a Nazi official.

Sources:

The Third Reich at War by Richard Evans

Nuremberg: Infamy on Trial by Joseph Persico

Albert Speer's Cross examination testimony