For one, it's much easier to maintain complicated rules in Sieve than with Gmail rules. This is just a function of having multiple lines and comments for rules.

I use Sieve to push a summary of certain messages to my phone (with https://pushover.net, another great service). This is not possible with Gmail rules (you can forward an entire message, but not selectively send just the subject and sender). See https://www.fastmail.fm/docs/sieve/fm-sieve-notify.html

Sieve also supports regular expressions: https://www.fastmail.fm/docs/sieve/draft-murchison-sieve-reg...

There are some example Sieve scripts that might give you a better idea of what Sieve can do:

http://ballz.ababa.net/jerry/sieve.txt

http://fastmail.wikia.com/wiki/MichaelKloseSieveScript

Note that you don't have to do all that crazy spam stuff -- the build in spam filtering seems to work fine for me. The only manual rule I added was to spam anything with common Russian characters because Russian spam was somehow slipping through the filter.