Elixir Nanoweb offers a much brighter tone than Elixir Polyweb. This is due to the thinner coating on the strings. Nanoweb strings have that "brand new" sound for weeks. I've found that the coating on nanoweb strings wears out much faster than the Polyweb strings. I would only recommend nanoweb strings to people who love that "new set of strings" sound from their guitar. They may not last as long as Polyweb strings, but Nanoweb strings last much longer than regular non-coated guitar strings. 

Nanoweb strings come in two different sub-flavors. You can get them in 80/20 bronze and phosphor bronze flavors. The phosphor bronze offers a warmer tone, while the 80/20 bronze has a brighter sound. For Nanoweb, I prefer the phosphor bronze. 

Here is an example of the nanoweb strings in action:

The Nanoweb strings aren't my favorite, but there are plenty of people who prefer them to the Polyweb. The coating is thinner so they have a much more "natural" sound. Yet, they still offer a lot of protection against finger crud. They are also easier to play than conventional strings, due to the coating. It lowers string friction.