Both would most likely experience the same things, but at different times. The Germans routinely rotated units out of the eastern front to rest, refit, accept new equipment (and train in new tactics and learn to use new Equipment) and new recruits and other reinforcements and in many cases be rebuilt as units after devastating casualties.
The 6. Panzer-division, for example, partook in Operation Barbarossa and the drive on Moscow in the winter. In May 1942 it was withdrawn to France to be rebuilt after suffering high casualties and returned to the eastern front in time to take part in the attempt to relieve Stalingrad.
That said, not all units ended up in western Europe. Many were sent to rear areas in the Soviet Union to do anti-partisan and occupation duties and be placed in reserve while they rested and refitted. In fact, most of the German losses in armour at Kursk happened during the Soviet counter-offensive, which over-ran the field repair shops where much of the German armour was in for service and repairs after the battle and many weakened German formations ended up in the way of the Soviet offensive.
In western Europe, the German Soldiers could enjoy good infrastructure, reliable mail communication with their friends and relatives back home, secure leave for home and relative low-risk occupational duties, as the resistance mostly smuggled out downed allied air men and expanded their organisation to spring into action once the allied invasion happened. The Germans had also set the exchange rate of the reichsmark to about three times as high to the French franc as it had been in 1930 (well after the reichsmark had recovered from the hyperinflation), which meant that a German soldier in western Europe could buy a lot of things - including expensive luxuries - on his otherwise meagre soldier's pay.
A soldier in garrison or occupational duties (note that the Heer did not man internment camps, only POW camps) would have access to three meals a day (which could be hard to get for a soldier on the frontline every day), sleep in requisitioned houses or barracks rather than tents, ahev regular access to mail, hygiene facilities and uniform washing, including lice extermination. Brothels were common and how the local military authorities handled them differed from accepted (including military medical personell checking for STDs regularly and 'clearing' prostitutes) to outright banned (but still existing).
Soldiers in occupation or garrison duty would often work on field fortifications, help haul supplies, build barracks and other facilities, help clear or repair destroyed infrastructure as well as working on training and equipment maintenance.
Patrols, suffering the occassional air raid, partisan raid, resistance attack, long range enemy patrol, hunting partisans, war crimes (such as shooting civilians as reprisals for partisan attacks), foraging (ie organised plundering of the countryside) and handling prisoners could also happen.
Bottom line is that it varied a lot depending on wether the German Soldier was stationed in western Europe or not, wether or not his unit was in reserve or on occupational duty, if his unit occupied a country where the Germans behaved decently (western Europe, Denmark, Norway, the Baltic states and Bohemia mostly) or commited lots of war crimes (Greece, Poland, Yugoslavia, the Soviet Union).