Range - In order to get reasonable sensitivity and confirm the range of gyro is within in your are expecting, meanwhile make sure the max angular rate of gyros are not exceed you are expecting .
Interface - Actually it has not too much difference in this section, most of gyros what we have feature an analog output, less gyro has a digital interface -either SPI or I2C.
Number of axes measured - Gyros are a little behind curve when it compared with accelerometers, most of gyros are either1 or 2 axis before 3 axis appeared on the market. You need to pay more attention to which of the three axes the gyro will measure. For example, some two axis gyros will measure pitch and roll, but others measure pitch and heading.
Power Usage – You have to consider how much the power of gyro will consume if your project is battery powered. Usually the request of current consumption should be within100s of μA range.