There are practical considerations: How easy to use? How fast? How easy is it to produce a different sequence of random numbers? How easy is it to replay the random numbers (for example, if you generated 10 billion random numbers, can you generate the exact same 10 billion random numbers again?)
The big question: Do the numbers generated behave like a sequence of random numbers? The first PRNG that I ever used had the bizarre property that of two consecutive values, the second was larger with probability about 0.6. Not very random. So you can run all kinds of statistical tests and check if your random number generator behaves in a random way. The more it behaves like random, the better.
And then comes cryptographical randomness. If I give you the last n random numbers, and complete knowledge how the random number generator behaves, can you predict the next random number? If yes, that makes it unsuitable in situations where you have adversaries.