location vs. rewite

[etrader]

I want to server favicon from a different place rather than the root folder.
As I explored I have two options

1. 
location = /favicon.ico { alias /var/www/media/images/favicon.X.ico; }

2.
rewrite ^/favicon.ico /var/www/media/images/favicon.X.ico last;

As I understand the second one needs an additional regex check for every
request to check if the url is favicon or not (imagine that we have a rewite
of ^/(.*)\.(.*) and thus the favicon rewite must be first).

How the location works? Does it also should be checked on every request?

In general, which solution is better ?

Posted at Nginx Forum: http://forum.nginx.org/read.php?2,238002,238002#msg-238002