So, you can tell they're there but not how many nor with what equipment, you can't do much to them indirectly, and your best combat equipment is neutralized by the city environment. You gotta go in and clear them out man-to-man, giving up whatever advantages you'd ordinarily have as the attacker to dig them out building by building and floor by floor, in the process taking at best equal losses from an enemy that in more open terrain might be easily overwhelmed.

For those reasons, cities are generally avoided on the offense, since it takes a disproportionate amount of force and time to drive out defenders and generally costs you as much as or more than it costs the enemy. However, they are great for the defensive, because if you can withdraw a big enough force into the city, you can threaten the enemy from flank or rear if he chooses to avoid you. He can either deplete his attack force by stationing a large rearguard against you, stall his attack while he roots you out, or continue forward with the risk that you'll roll out to cut his supply lines at a bad time. Also, cities are often located at important intersections of rail or highway; in some terrain, those intersections might be vital enough that the city must be taken in order to maintain a route of advance. In the modern era, cities might contain airports that can be converted to support military aircraft and used to bring in supplies and reinforcements for the ground troops of whoever holds the airport. Doesn't do to let the enemy operate an airfield in your rear.

Among other things, Stalingrad had heavy industry, including a tank works that actually continued operation through much of the battle. Tanks would roll off the line, get supplied, and then roll straight into battle - unpainted - against the Nazis. Capturing that industry would have reduced the Russians' ability to arm their troops. Stalingrad also had a major river running through the middle of it - the Volga: holding the city would have denied the Russians the ability to use that river for transport between the Caspian Sea and Northern Russia. Finally, holding Stalingrad would secure the German flank in the larger strategic theater, presenting the Russians in turn with the problem of reducing an army in a city if they wanted to attack on that flank - which would probably mean that the Russians would choose to attack elsewhere. Limiting the enemy's options makes him more predictable and easier to counter.