I would use an exact replacement if you can find the spec's.
I work a lot with Metal Halide bulbs in my other hobby, Reef Tank Aquariums, and often a particular type of bulb has to be matched *exactly* to a type of ballast. Starting voltage, open circuit voltage, can all be different. Different wattage of bulbs have different voltages.
However, it's possible that projector bulbs are all the same kind but my gut feeling is that they are not.