How did conditions in Nazi labor camps and the Gulag compare?

Analysis at the level of personal narratives will be counter productive.

Both systems combined "industrial" and "punitive" (punishment) systems. Both industrial systems followed an internal logic of productivity, to the point of literally paying their prisoners, wether in subsistence, kind or coin. Both systems did not know a method of organisation of labour other than wage labour. The price of labour in both systems in the 1930s and 1940s fell below the cost of the long term and immediate reproduction of labour: no kids would feasibly survive to reproduce the employee pool; the workers themselves would be worked to death. The soviet system differed in having nominal end-of-sentence dates, but this was nominal due to the "double" system, and due to "closed" camps. (By the mid 1950s after mass prison workers strikes and revolutions in Soviet-aligned countries for workers control, the Soviet Union returned the gulags to a system of merely horrific and unmentionable labour camps, where most workers were predicted to bodily survive their sentence.)

Neither camp system ran at a profit in terms of the external ("non-camp") economy, both systems were massive economic drains on their capitalist societies.

Both camp systems involved liquidation camps. The German liquidation camps were aimed primarily at the racial other, and primarily liquidated Soviet Citizens, Jews and Roma. The test case for liquidation was the mass starvation of Soviet POWs. Generally, however, Soviet Citizens were worked to death or murdered outside of camps, including Jewish soviet citizens. The German liquidation camps were organised to make the mass killing of humans as comprehensible to the murderers as possible, due to the failure of the Einsatzgruppen ("action groups," action here meaning mass shooting) due to mental illness.

In contrast Soviet liquidations were of two types. Primarily: the wages of gulag inmates were reduced during WWII to below the capacity to reproduce labour within six month or twelve month time frames. Like the sugar islands of early capitalism workers were literally starved to death or disease leading to death. This system of death did not exist in the 1930s prior to the war, or after the 1940s when the war's consequences reduced inside the Soviet Union. It appears due to the generally non-racial imposition of unjust, undue and arbitrary punishment that the Soviet camps were not aimed at generalised racial liquidation, but rather at generally terrorising soviet citizens, or punishing imaginary political enemies who did not actually exist.

The other mass murders in the Soviet camps was of the "closed camps." Here prisoners were not known to be kept, but posting mail to them succeeded. After a certain point during the early war all mail was returned to sender as undeliverable. This and other clues indicate that the inmates of the closed camps were murdered wholesale during 1941 in a political panic. Closed camp prisoners were generally political prisoners viewed as capable of real action against the party: former party members or members of former parties. This universal liquidation of a class of prisoners was not repeated.

The lines of fracture between the camp systems are motivational:

• Soviet - imaginary political enemies and the working class (including the post enclosure rural working class) as an actual political enemy;
• Germans - imaginary racial enemies, and Yugoslav, Pole and Soviet Citizens as actual enemies viewed through a racial lens;—

and, they are operational

• Both camps generally used an industrial model of capitalism and worker which was used to motivate labour; both camps set the price of labour below the general price of labour; both camps did at times set the price of labour below the actual price of keeping labourers alive. The Soviet camp system differed in that it did so during a massive economic crisis, and doing so was viewed as a lamentable but necessary contingency. The German system viewed setting the price of labour at the point labour would die as a benefit.
• Neither camp system produced a profit in society. However the Gulag was politically successful, the labour and death camps were not.
• • To the extent that gulag was part of a successful system of limiting urban and working class discontent, particularly after WWII in soviet-aligned european societies; gulag also worked in the interests of its ruling class. No profit was made but a political benefit was felt.
• • To the extent that Germans wished to punish the imaginary Slav, Jew and Roma with death. And to the extent that both firstly non-Einsatzgruppen mass shooting in "actions," and secondly also "death marches" both killed about the same numbers as camps; camps were an optional extra which failed to achieve the policy aim of the society (genocide and near total genocide), and which also failed to do so efficiently: competitive options were available and had similar throughputs while also achieving secondary benefits such as occasionally killing partisans, or retreating into the heart of a dying beast trying desperately to hide the evidence of your horrific barbarity.

Bibliography

Given that this question asks after literary sources, the master work of literary engagement with Gulag is, without a doubt or double, Solzhenitsyn Archipelago: An Experiment in Literary Investigation. Please pay especial attention to the subtitle. Solzhenitsyn must be read if you're going to work in this area, but you must be aware that he is a novellist with severe religious motivations, and that his motivation is literary, his method is literary, and he is no historian.

Applebaum is a journalist.

Most of my historical reading is in the Hungarian camp system. This is indicative, but not determinate. The Soviet camp system's life 1938-1948 is a significant moment. Washing Stalin's wounds with the relative "humanity" of the gulag 1948 to 1954 is painting a sepulchure. More indicative is Gulag after the strikes, 1955-1960, and the 'gulag' 1960-1993. Here the Soviet ruling class was only as barbarous as the soviet working class would tolerate, and it looks as horific as US racial labour incarceration or Chinese labour incarceration.

In contrast the Germans got to do what they wanted in the 1940s. I would suggest not reading camps first. Goldhagen is as well respected by historians as Applebaum, but unlike Applebaum in his non-analytical narrative provides a standard account of how Germans killed millions of people in the holocaust; historians disagree with his "why." I recommend starting with Browning's Ordinary Men as this represents the far more normal action of Germans against their racial imaginary.

This is to restate: Gulag was one policy tool for class rule in the Soviet Union. Camps were one weapon of mass murder in the Germany fantasy of annihilation.