Which version is best for bioinformatician to work on?
Which version you ought to use is mostly dependent on what you want to get done.
If you can do exactly what you want with Python 3.x, great! There's a few downsides, such as comparatively limited library support and the fact that most current Linux distributions and Macs are still using 2.x as default, but as a language Python 3.x is definitely ready. As long as actually getting Python 3.x on your user's computers and you're writing things where lack of third-party software isn't a major impediment, Python 3.x is an excellent choice.
However, as a Bioinformatician there are some key issues that may require you to use Python 2 rather than Python 3.
Firstly, if you're deploying to an environment you don't control, that may impose a specific version, rather than allowing you a free selection from the available versions.
Secondly, if you want to use a specific third party package or utility that doesn't yet have a released version that is compatible with Python 3, and porting that package is a non-trivial task, you may choose to use Python 2 in order to retain access to that package.
For Bioinformatics based analysis there are several python packages/modules available which are mostly incompatable with Python3, therefore I recommend to use the old version for the time being.