Broadly speaking, yes, attitudes towards the SS were significantly harsher than those towards the regular army, the Wehrmacht. In many lower level units there was an unwritten (and in at least one instance written) policy that SS troops were simply not to be taken prisoner. However it should be noted using the word 'sympathy' to describe the troops attitude towards the Wehrmacht would be stretching it a little.
There are two main reasons for the attitude towards the SS:
Firstly well before the events portrayed in the movie the SS had acquired a bad reputation having been implicated in a number of massacres of allied troops and civilians. The massacre of Canadian troops by the 12th SS and the Malmedy massacre during the Battle of Bulge are just two of the better known atrocities.
Secondly as the war entered it's final stage and the allies entered Germany there was widespread anger that the Germans were continuing to fight even when their position was hopeless. Broadly speaking again, it was the SS putting up a significant amount of resistance, with many Wehrmacht troops simply looking for the safest moment to surrender. At this point the SS felt that they were fighting for their lives and did not expect to be taken prisoner.
Principle source : The Guns At Last Light by Rick Atkinson. This book I have on my Kindle so I can look up references. The others are on the book shelf at home.
I don't know if the OP means just the Western Allies or the USSR as well, but the Soviets did have a special hatred for the SS in particular. German POWs often immediately met accusations of "Du SS!". Captured SS were usually shot on the spot.
However, the Soviets were in no way "sympathetic" to regular soldiers. After the Wehrmacht's atrocities in the East and relentless anti-German propaganda, Soviet attitudes towards all Germans (particularly men) were very harsh. Captured Germans not shot immediately could expect a spell in the Gulag.
The Wehrmacht knew this, and often fought bitterly so they could surrender to the Americans. For example, Wenck fought a desperate battle to escape a Soviet encirclement and get his men across the Elbe.
Source: Berlin by Antony Beevor