First of all, I have to say that it's just beautiful. The Twitter clients that support customizations usually have a dark and a light theme to choose from. Not Brink. You can theme it with backgrounds and fonts, you can have multiple accounts, and you can even add a tile to post updates from the start screen with one tap.
Another thing I absolutely love about it is the Activity view. With Seesmic I used to have a section for mentions and one for retweets which I had to go back and forth through. This Activity view shows both mentions and retweets and I like it. Maybe it's just me, but the way I need to use Twitter, Brink is what I need.
Oh, did I mention it's free AND ad-free? I would actually pay for this app(if MS would hurry up to add support for payment from Romania that is).
One more thing I like about Brink the attention to detail. Those little things that just tick all the boxes. One example retweet style. You can choose from quote, append and pre-pend and you can use which one you like best. Some features you only get with paid clients are support for both Instapaper and Pocket(read it later), support for Bitly and for Flickr.
Another thing that I love about it is the way they do lists. Most clients, official one included, just show you the members of Twitter your lists in their lists views. Brink shows you their tweets.
The only two features I would like to see, and I was assured by the developer of the app that they are well underway, are toast and live tile notifications. Once those arrive, I will no longer have a reason to keep the official Twitter client installed on my phone.
Anyways, here's a video tour of the app. Go on, download it yourself, it's definitely worth it.