Version 1.0.6 is the current stable version. But it has no support for the Arduino Due or Yun yet.
The 1.5.7 BETA is the version in development. It has also support for the Due and the Yun. However, a lot changes and improvements has been made, so there might be a bug in it.
Parts of the 1.5.7 BETA has already been used to update 1.0.5 to 1.0.6. So the normal version benefits from the development.
I like the 1.5.7 version because it uses a new avr-gcc compiler. And I have not encountered any problem with it. In fact, it works a lot better with improvements for the Java serial communication.
To the Arduino team - You need to re-evaluate this number system because it just doesn't make any sense, and does lead to confusion. The number system is very unlike any I've seen before. Pick a number, make that the stable version (and forget 'codenames' as they make the confusion worse). Then, when you release a beta you advance the stable version number and put Beta at the end of it. When you're out of beta then remove the link to the beta version. That way the numbers keep climbing and the beta/stable versions are clearly distinguishable.