About pyjamas maturity vs GWT maturity (with short dead lines) for a web application
In fact, from my beginner point of
  view, it seems like the python world
  is more suitable for a
  quickly-developed and fun web
  application. And, on the other hand,
  the java world is useful for
  performance-oriented, scalable
  solutions and for 'serious' projects
  with big money involved...

Naah.  For example, YouTube is in Python -- where do you see that affecting its performance, scalability, or "big money" characteristics?

Is pyjamas mature enough to replace
  GWT on a performance and functionality
  point of view?

Completely different question from the previous, silly observation.
GWT has been around for longer, and has more users and contributors.  Perhaps pyjamas is "good enough" for many uses -- nevertheless, it is at release 0.7, with GWT at release 2.0, which can be taken as an indication that GWT is better, more developed and mature.
Most real-world, highly-scalable web apps use "real" Javascript (typically with some supporting framework, such as the very popular jQuery or any of its many "competitors"); if, for whatever reason, you can't (or, more likely, don't want to), then GWT is probably a less risky choice than pyjamas, in my opinion.
I love both, python and Java and I have this first 'serious' web application project that I would like to carry out. 
I find it hard to choose between pyjamas + django and GWT + Hibernate.
In fact, from my beginner point of view, it seems like the python world is more suitable for a quickly-developed and fun web application. 
And, on the other hand, the java world is useful for performance-oriented, scalable solutions and for 'serious' projects with big money involved...
My requirements are quite simple: this application has to replace a desktop application. So, the performance factor is there. But my deadlines are pretty short.
Is pyjamas mature enough to replace GWT on a performance and functionality point of view?