Two schools of thought on DHCP.

I am setting up a new network for a client with a DC and file server. All users are allowed internet access.
What is the opinion regarding using the router to perform DHCP vs using a Win2003 DC?
If you use the router then workstations are connected more or less directly to the gateway router. But if you use the DC you must access the DC to access the internet.
Is there a big performance hit if the DC has to perform DHCP and manage internet connections?