Will start with the tl;dr: by the time German soldiers were in a position to have to seriously debate whether or not to die or surrender they had managed to supremely piss the soviets off. They would have faced horrendous treatment so they may have felt death was better. Soviet hatred for fascism was so intense that surrender was a risky proposition if you didn't want to risk just getting lynched by the soldiers you surrender to, if you're lucky you might make it to a camp where you will face up to a 1/3 chance of being worked to death or disappeared. Surrender to the West and go on holiday to US or Canada as they didn't want to keep many prisoners in the UK though some did stay there.
Longer, but for the sake of brevity I'm going to use American numbers considering of the Western Allies they were the "worst":
So if you didn't already know the Germans had mistreated soviet prisoners, and their treatment of occupied areas wasn't exactly stellar now was it? This tends to be bad for mutual prisoner standards. From what I will try to source for you the Germans looked down heavily on Soviet POWs as subhuman, they were starved and often left to essentially fend for themselves inside camps while western POWs were treated with the rights a POW should have. Pulling things like the Katyn massacre would not help your image in an already brutal war, and the eastern front was extremely brutal. See edit below, thanks to /u/Musthaveaname for pointing this out.
Their treatment once capture would warrant thought as to whether they wished to be abused themselves and possibly executed either directly or by work until death anyway or just fight until you were killed. You just need to have a look at the figures for German POWs in soviet camps to see how bad things were, according to Maschke and Overman anywhere between 700,000-1,000,000 Germans died in Soviet custody. That is out of around 3,000,000 total German prisoners taken into Soviet custody.
Edit, relocated: Pulling things like the Katyn massacre would not help your image in an already brutal war, and the eastern front was extremely brutal. When the Germans found the bodies there and the efforts to hide it all it doesn't make you feel like it's a good idea to surrender, you will not be given no quarter. The war in the East was brutal, but finding all those bodies doesn't make it seem like your enemy will stop when you surrender.
The Americans on the other hand took on 5,000,000 prisoners for a maximum estimated loss of 1.1% according to Cowdrey and that sits with Bohme's 1%. According to the U.S. Provost Marshall feel they lost less than that, however due to the chaos of taking in large amounts of prisoners near the end of the war some records are just flawed. From many accounts life in Western POW camps was rather enjoyable, you'd eat well enough, live in conditions found fair, have education and entertainment programmes. I can't source them, but I have read accounts from Germans who said they preferred their time in American camps to their lives post war especially if they returned to what became East Germany.
British, which included Canada, POW death rates were even lower.
Some further reading for you:
James Bacque, Other losses, 1989, ISBN 0-7737-2269-6
Erich Maschke, Zur Geschichte der deutschen Kriegsgefangenen des Zweiten Weltkrieges Bielefeld, E. und W. Gieseking, 1962-1974 Vol 15 P 185-230
this is largely true, on all levels. Goebbels fell out with Hitler during the last days of the Reich for making secret peace accords to the western allies behind Hitler's back. Meanwhile, huge huge numbers of people both soldiers and civilians were streaming westwards away from the Soviets in the hope of reaching British or American lines.
Nazi propaganda played a role in this to be sure and is one of the few times when Nazi propaganda actually matched up with facts on the ground. Capture by the Red Army was widely broadcast as a one way ticket to being shot on the spot, yet the Nazi's also stepped up an intense and effective propaganda campaign pointing out that if German soldiers failed in their duty and allowed Germany to be occupied by the Soviets then the horrors inflicted by the Wehrmacht in Russia would be repaid in full by the advancing Soviets.
This was extremely successful as the vast majority of soldiers in the Wehrmacht knew exactly what had happened in Russia, the burning of villages and the massacre of Russian civilians, and no-one wanted that to happen to their families. Thus resistance was strengthened nut this had a major downside, by failing to highlight the danger posed by the USA (or fabricating the danger if you will) it just meant that rather than fighting on all fronts to the last man, the western front became the ticket to life and safety for millions of German soldiers and civilians.
The fact that Stalin thought the Nazi's were purposefully offering no resistance to the Western Allies points to the scale of the surrenders. In turn this slightly backfired as Stalin, now driven by paranoia of Eisenhower reaching Berlin first ordered the Red Army to relentlessly press the advance, which in turn resulted in much more brutal fighting, causing great losses in Soviet forces which only further enraged them and thus resulted in a rise in atrocities. which in turn caused more Germans to try and flee westwards.
Sources: Antony Beevor; Berlin and The Second World War.