What happens if positrons, instead of electrons, are decelerated inside an X-ray tube?

I would say there will be a huge effect. I am not sure if acceleration vs. deceleration is very important, but there will also be gamma radiation due to annihilation of the positrons with electrons of the matter.

EDIT: (11/25/2016) As for Bremsstrahlung of positrons, see https://arxiv.org/abs/1209.5532 (Abstract: Fully relativistic treatment of the electron-atom and positron-atom bremsstrahlung is reported. The calculation is based on the partial-wave expansion of the Dirac scattering states in an external atomic field. A comparison of the electron and positron bremsstrahlung is presented for the single and double differential cross sections and the Stokes parameters of the emitted photon. It is demonstrated that the electron-positron symmetry of the bremsstrahlung spectra, which is nearly exact in the nonrelativistic regime, is to a large extent removed by the relativistic effects.)