I am thinking about how to build advertise site which works like twitter.

That means, most user don't not visit the site by browser, they should run a dedicated client application on their PC or smart phone. Then they set some filters about what kind of advertise they like. And when new post that fulfill their needs appear, the client will make a notification.
To make that client as real time as possible, it has to poll the server within a short time interval.

The problem is, should I do the filtering at the server side when client polls, or should I simply transfer all new posts to client and let client do the filtering?

Making server side filtering might cause too much CPU cycles of server, but transferring every post blindly to client might waste a lot of bandwidth.

Just a brain game. :)