Hi,
Very shortly, ip default-network should not be used at all today. It was used in old IGRP years and years back - its purpose was to flag a specific classful network not belonging to your autonomous system as a "candidate default network". The path toward this "candidate default network" was then also used as a path toward the default route. However, the use of ip default-network required you to redistribute this classful network into IGRP or EIGRP, and have it flagged with this command on the router that performed the redistribution. The command did not really work with classless networks (there were some nasty hacks around it), and all in all, it is truly a fossil of ages past that is best forgotten.
Today, we should always use the 0.0.0.0/0 as the default route, and because - sadly - EIGRP still does not support the default-information originate command, the easiest way to inject this route into EIGRP is to redistribute it.
You might be interested in reading the following document, too:
https://www.cisco.com/c/en/us/support/docs/ip/routing-information-protocol-rip/16448-default.html
Feel welcome to ask further!
Best regards,
Peter
