The Etherswitch card (NM-16ESW) is a LAN switch. It cannot by itself route between its ports, but the router into which it's installed can route between the ports.
So I guess the answer is "both". See:
EtherSwitch Network and Service Modules on 2600/3600/3700 Series Routers FAQ
Q. Can you configure a port on the EtherSwitch module as a routed port? A. With the release of Cisco IOS® Software Releases 12.2(15)ZJ and
12.3(4)T, you can assign an IP address directly to ports of the EtherSwitch module. This feature makes those ports Layer 3 (L3) or routed ports. These ports cannot receive a DHCP address, and the ports do not support subinterfaces. L3 traffic on the routed ports still requires that the traffic utilize the platform routing engine. No L3 switching occurs on the blade. You can use all routing protocols in conjunction with this feature. This configuration serves as an example: interface FastEthernet1/0 no switchport ip address 172.16.1.0 255.255.0.0
You can also create SVIs (VLAN interfaces) to route among VLANs (or in addition to) among ports.
Do be aware of the platform switching (PPS) limitations,