Why do tungsten and chromium have different electronic configurations?
Firstly note that the energetic differences between $\mathrm d^m\mathrm s^n$ and $\mathrm d^{m-1}\mathrm s^{n+1}$ configurations are generally not large. Sometimes these are not amenable to simple qualitative rationalisation.

However in this case it is possible to argue along two lines.


Relativistic effects lead to the stabilisation of the 6s subshell and destabilisation of the 5d subshell, which directly favours population of 6s over 5d.
Electron-electron repulsions in the 3d/4s orbitals are generally larger than repulsions in the 5d/6s orbitals, because the latter are more diffuse. Hence chromium chooses to adopt a configuration in which exchange energy is maximised (i.e. electron-electron repulsions are minimised).