How prestigious is a Microsoft Research scholarship This question is intended to be analogous to the Fulbright one; however, the Microsoft Research scholarship would be for a PhD.

How may this scholarship influence one's possibilities to work in the academia or in the industry? How does it compare, e.g. in terms of prestige and academia/industry opportunities, against the Fulbright? Is the scholarship prestigious in the US, UK or on a world wide scale  (especially if it is for a PhD in the UK)?
Instead of worrying about how prestigious the award is on its own, ask yourself what type of research you're going to conduct using the funds. In the end, nobody will care that your research was funded by Microsoft or Google or the NSF (or whatever the UK version of that is); they'll care about the contribution you're making to the field.

Nobody is going to stop you at a job talk and say, "Well, your research is amazing, but I think you should have applied for funding from X-Company."

Barring any ethical issues, funding is funding. As long as you put it to good use, you should be in good shape!