While others can answer about the battles of Stalingrad, Sevastopol, and Berlin, perhaps the closest analogue to Mosul would be the US Army and its experiences.

The first thing you should understand is that maneuver over urban terrain, or MOUT, is historically considered the least desirable option by the US military. Part of this is shaped by Americans' reticence for casualties, both friendly and enemy, and urban combat is very casualty-intense. As such, there actually aren't very many instances in World War II of American forces engaging in urban combat. One exception is the Battle of Aachen.

The reason the Americans had to fight in Aachen was because the city was located on VII Corps flank after it made a small penetration into the Siegfried Line, a network of defenses on the German-French border. As such, the Americans were forced to reduce Aachen to eliminate that threat. For the task, the 1st and 30th Infantry Divisions were selected, both veterans from the D-Day Campaign. No specific doctrine existed in the US Army for Urban Operations. Instead, both US infantry divisions were highly adept at fire-and-maneuver, which emphasizes combined-arms firepower to reduce and suppress the adversary before making contact. The US commanders made the decision to advance into the city methodically, tightly controlling subunits' rate of advance to prevent the lines from becoming blurred and neutralizing the American firepower advantage. They also made the decision to not spare the city, and there was no upper bound of collateral damage. As such the Americans made liberal use of artillery to reduce German strong points, outright destroying buildings whenever possible. Even with this precaution, all told American casualties totaled 5,000, equal to the Germans, and significant portions of Aachen were destroyed most of which were because of American firepower. Notably, the Battle of Manila was resolved in similar fashion, with General MacArthur relaxing his initial tight control of heavy weapons to reduce his own casualties at the cost of heavy destruction of the Philippine capital.

You can draw a few parallels between Mosul and Aachen. In both cases, rapidity of advance was sacrificed for a reduction of casualties and enabling firepower advantage. There might have been a greater emphasis on reducing casualties in Mosul than there might have been in Aachen, and almost certainly greater care was taken to limit wanton destruction of property. In general the Eastern Front battles like Stalingrad were more casualty intense as the Soviets preferred to have their troops in close contact with the enemy. In the case of Stalingrad it was because the Germans held air and artillery superiority, and in the case of Berlin it was due to political pressure to bring about a rapid conquest of the German capital.