Pros of IDNs:
Having the IDN allows you to keep control of your brand/corporate identity.
Easy to type in for native speakers.
Cons of IDNs:
Not all email boxes or web browsers support non ASCII characters.
Security issues: homograph spoofing. It is easy to take a real domain and create a spoof with different Unicode letters that are seemingly the same. For example the letter ‘a’ can be U+0061 (Latin ‘a’) or U+0430 (Cyrillic ‘a’). A visitor would never see the different in these letters while typing, thus creating a major security problem for websites.
Most keyboards do not have special characters, so it can confuse visitors.