In addition to what you can find here : Choosing power supply, how to get the voltage and current ratings?
I would say that the voltage ripple of the output is a criteria.
You will use it for audio applications. Some low cost very noisy power switched mode power supplies may be too noisy for audio applications. You may hear added noise to the audio.
If you buy high end power supplies, you will find graph and figures about the voltage ripple. The ideal goal would be to select a new power supply with a ripple less than, or equal to, the original one. Unfortunately, you can't know the voltage ripple of the "official" power supply... The only thing you can do is to buy one that seems to be better than the average you find.
Another parameter is safety. Your pedal is connected to something that is in contact with a human body. Thus, low cost poorly designed power supplies may be risky to use. I suggest to choose a well known brand, or one that is meant for medical applications. It may be overprized, but my safety has an even higher price....