Hi Lee,
Greetings!
As patrick said, the cisco 7600 is basically a high end router while the cisco 6500 though also capable of multi-layer switching is more of a high end switch.
As defined by Cisco, the 7600 Series combines optical WAN/MAN networking and high-volume Ethernet aggregation with a focus on the delivery of high-touch services for the IP and MPLS edge. It combines Layer 2 and Layer 3 networking capabilities with a high-bandwidth, high performance architecture including hardware-based forwarding of MPLS, IPv4 and IPv6. Each router can deliver DS0 to OC-48 WAN and Nx10-Mbps Ethernet to Nx10-Gigabit Ethernet connectivity into service provider edge, metropolitan-area and enterprise networks for a variety of triple-play and aggregation solutions.
On the other hand, the 6500 family delivers highly available secure converged network services for Enterprise and Service Provider networks. It is designed to address increased requirements for gigabit scalability, high-availability, rich services, and multilayer switching in backbone distribution, and wiring closet topology as well as datacenter environments.
Generally, both supports several modules and supervisor cards so probably, to be able to decide on which to use is to identify your purpose. If you are a service provider setting up an IP core network, the 7600 well suites your needs. But for an enterprise setting up a core network or a datacenter, the 6500 series is very well enough. The high-availability features of the 6500 series switches is also a plus for datacenters or networks where resiliency and availabilty is a big factor.
Hope this helps, regards,
Albert
