Why are overhead electric wires allowed to have higher voltages than third rails for rapid transit railways?
According to answers to this question: 


  The breakdown voltage of air varies significantly due to changes in
  humidity, pressure, and temperature. However, a rough guide is that it
  takes 1 kV per millimeter.


Therefore your 25 kV overhead rods will be adequately spaced from the ceiling at a minimum of 25 mm / 1 inch; it looks like they have several times that.

The main reason for using lower voltages on 3rd rail systems is probably the size of the insulators to support the rail mechanically. Insulators aren't free air clearance; as the answer explains:


  The breakdown gradient for creepage is lower than for clearance since
  dirt can accumulate on surfaces. Some dirt is partially conductive on
  its own, but many things can provide leakage paths after soaking up
  some humidity.


Your second photo of the tunnel appears to show the clearance from the ceiling is rather less than the creepage distance along the horizontal insulators. It would be impossible to mount a third rail on insulators of that size. 

The safety of line personnel on 3rd rail is a factor for the lower voltage, but not the only one: direct contact with a 3rd rail at less than 1 kV is likely to be fatal to a human.