In my humble opinion, the answer to this question will greatly depend on the type of game you intend to create.
Given that browser-based 3D games necessitate careful attention to memory management, assets, and more, I believe the optimal framework for your game would be one that you custom-build.
You will inevitably face a balancing act between quality and performance, regardless of the framework selected.
As for available options: at present, there are few complete game frameworks based on three.js.
In my view, your best options include
- starting with a reputable "base" library such as Physijs and expanding from there
- utilizing existing building blocks created by others, like J.Etienne's three.js extras
- beginning with an open-source "finished" project like voxeljs or cubeslam
Essentially, do some searching on GitHub to discover resources aligned with your specific objectives.
Alternatively, if you're feeling adventurous, consider lending a hand with my own modest framework here. Yes, I shamelessly promoted it.