This is just going to go on and on isnt it...
Steel is heavy - but very strong so less material is used, steel is very good with compression (compactive) forces and tension (stretching). Steel frames are relatively simple to construct. Steel frames can be built quickly but the steel sections have to be procured (built) first - this can take many, many months (At least 6 months - probably much longer) . Steel frames traditionally are less able to resist wind forces and hence have to be braced with diagonal members and shear walls. However the diagrid method of the cctv tower is very rigid.
Concrete is light weight, concrete is good at resisting compressive forces but can not resist tensile (stretching) forces at all - for this reason concrete frames are usually reinforced with steel bars, the steel bars will resist the tension forces and prevent cracking in the concrete. Concrete frames naturally resist wind loads very well, concrete frames are more complicated to build - they require 'formwork' to be built - these are the shutters that the concrete is poured into so that it can archive its shape. Concrete can be made into any shape. Concrete frames do take longer to build - as they take time to set etc, however there is no procurement process so construction can start sooner.
In reality there is very little between the two methods - looking at skyscrapers you can not say most of them are concrete frame or most are steel. The empire state building is steel framed, the gherkin in london is steel, the Petronas twin towers are concrete etc etc.
One of the main factors is cost - this depends on the availability and location of the raw materials, china is has a large production of steel, hence it may be more cost beneficial for them to use steel.
Also with the CCTV building it has that enormous overhang, so the tendancy is for that overhang to 'turn' over - to counter this the two towers have to try and 'pull' down on their end of the roof beam. This means there are enormous tension forces in the two towers - hence a very large amount of steel would be required in the towers to resist these forces.
I hope that answers some of the questions.