Flask has a bigger dev team, but Bottle is a nicer, more elegant micro-framework. From what I can see, the design of Flask can be broken down into 2 phases. The first phase is essentially like bottle. The second phase added class views and the likes. And it became inelegant and verbose.
If bottle has something like Flask's Blueprint, which facilitates the management of larger projects, bottle will clearly win as a micro-framework.
In the end, who is the winner really boils down to how much love a framework is given to by its founder. Web.py started a generation of nice frameworks, but I think the person behind it didn't put a lot of effort in pushing it forward, and eventually, it just stopped progressing.
Bottle is older than Flask still the latter is far more popular, has more features, is better documented and has a bigger community. It is really not a question of who will win but who has won.
Bottle supports Python 3 (as does CherryPy, Pyramid, and Tornado), while Flask currently doesn't. Depending on project requirements, this may or may not be important.
I hope they will continue to coexist. Competition is great. I personally prefer Flask, mostly because I built my own little framework on top of Werkzeug before and know the code quite well. Also, I'm not a huge fan of the single-file approach, but this is just my personal preference.
