In my opinion both phrases can be correct.

The main difference is in the nouns.

A building (noun) is a structure that can be used for 2 purposes. Residential - where people live, and Non-residential - where people work, learn and play, for example offices, workshops, meeting halls, sports halls, schools, hospitals. Generally the space is enclosed, it has a roof, walls and floors.

Normally construction is the work of building something. But it can sometimes be used to mean a building.

A construction (noun) can also be a dam, a football stadium, a tunnel, a bridge, a monument. So none of these are called buildings (noun), but you can build or construct them.

If you are describing something which has a roof, walls and floor, I would use "constructing a building"

If you talking about a major project, like the new Istanbul airport, with runways, and access roads, towers, and other buildings, it would be best to say "constructing an airport". You can also say "building an airport". Both are fine to use.

I hope this has not confused you. 

Very well explained. I like it very much. Thanks Henry.

ÇOK TEŞEKKÜR EDERİM