So firstly it helps a bit to understand some of the basic forces involved here. When you put weight on top of a beam, a slab, etc. that is only supported underneath in some places, it tends to want to bend downward in between its supports. You can see the effect of this yourself by taking a sheet of paper, holding it at both ends, and having someone else push down in the middle. Works the same with steel and concrete except it takes a lot more force to bend them.
Anyway, so as a result of this bending, the top of the beam/slab/etc. is getting pushed together ("compression", in technical terms) while the bottom is getting pulled apart ("tension", in technical terms).
One important fact about concrete: it's a lot better at withstanding compression than tension. Push it together and it takes a lot of force to crush it. Pull it apart and it crumbles under a lot less force.
Because of this, whenever concrete is used as a building material, it is always paired with some steel to carry that tensile force and prevent the concrete from crumbling.
The bridges where you're seeing a concrete surface on the bottom have steel rebar embedded within the deck.
Where you see corrugated steel on the bottom, this is known as a "composite deck" and that steel is not just a form for the concrete that was left in place - it is a substitute for embedding rebar within it, that corrugated steel is there to carry the tensile force at the bottom.
As for which is better, neither is inherently - both methods work. Any choice between one over the other may simply be a matter of which is less expensive at that particular time and place... or a preference by the designer or contractor as to which they are more familiar with.