Is it better to have routed interfaces between the two cores (Running EIGRP) or a port channel with No Passive Interface VLAN?
The answer is not which is better but first we need to understand the requirements. If you have the server(s) connected directly to these switches and they are dual-homed, then you need to run Layer2 between these switches.
If you don't have the need to share a Layer2 vlan between the switches, then go routed inter-switch links.
Just remember the requirements, you need to treat each switch like a router. For instance, you need to create Vlans on each switch and the IP range must not overlap.