The most important advantage of reinforced concrete over pure steel structure is availability. Many countries/regions on earth rely on imports for general goods production needs, the cost of steel can run prohibitively high compared to concrete.
The next advantage is weight. In certain types of structure weight counts, such as underwater powerhouse. However, for most buildings, weight is seen as a disadvantage. The last I can think of is better fire protection, without needing separate fireproofing material.
BlackSmith has raised an interesting point - shapes. The many different shapes of steel have their disadvantages:
Weaker in compression for buckling concerns.
Weaker in resisting torsion.
Escalate construction costs for fabrication, transporting (extra-long, wide elements navigating through crowded city centers), and erection (especially connections). Compared to reinforced concrete structures, the construction of steel structures often involves highly skilled laborers, and/or speciality trades. On the other hand, the reinforced concrete most often can settle on semi-skilled laborers.
Durability, longevity, and low maintenance - in certain environments such as water or oceanfront, corrosive environment, concrete structures are often outperformed steel structures. It is easier to maintain and repair, or restore to its original conditions.
Although the list of reinforced concrete advantages may get longer, we have to recongnize its main disadvantages that have greatly limited its usefulness in certain types of structures - self-weight, inflexibility (compared to structural steel), and its brittle nature. But it will always be here to stay for situations that can be benefitted from its advantages.