What is the difference between nexus and asr router?

it is totally different applications devices nexus mainly used for Data center and visualization cloud networks, and ASR mainly used for Service provider networking proposes.

for more  details please see the following links, and you are welcome any time.

http://www.cisco.com/c/en/us/products/switches/data-center-switches/index.html#~technologies

http://www.cisco.com/c/en/us/products/routers/asr--series-aggregation-services-routers/index.html

http://www.cisco.com/c/en/us/products/routers/asr--series-aggregation-services-routers/index.html