I guess that your question is case/system dependent. But in general, I see no real difference between a built-in and a module/card other than the specifications of each. For example, as you know, Fastethernet can give you a max of 100Mbps while Ethernet can do 10Mbps max. However, built-ins are supposed to be more integrated and well optimized from the performance point of view. Other than that, as long as the router and module/card are from the same manufacturer, it should work perfectly as well.
I might be wrong, so any one please add your experience.
One note here, some times a dual or quad Ethernet are actually dual/quad switch connected internally to one logical Ethernet port. So it's actually only one Ethernet port. An example of this is the PIX 501. It has two Ethernets with one of them connected to a 4 ports switch internally.