In fact payload fuzzing(intruding) feature works very well in Burp.
This wiki is about the manual testing of payload.
When I tested the fuzzing feature on ZAP I found that ZAP is not able to save the payload configurations.
Also actual creation of payloads for each string/position is little complex compared to Burp.
Even Burp does not handle 100% automation of payload requests even if we create its plugins i.e certain part we have to run manually.
Thanks,
Aadi