The Z1 is an audio hobbyist device in that you can swap out some components like opamps, doesn't have a display, etc. It is a minimalist device that, like the Walnut, attempts to deliver purity of sound without any special conveniences.
The T6/Rocker is a small device that offers loads of file compatibility along with a comprehensive display/menu system to easily access its feature set.
Both are built well for their respective purposes. For jogging and other athletic use, and choosing only between the two, I would opt for the T6/Rocker for form and functionality.
However, the Sandisk Clip Sport Plus is probably a better choice than those two players if the intended use is for exercise of any kind - it is much lighter, clips to clothing, has good file compatibility, decent sound, Bluetooth, FM radio, and most importantly, is water resistant by design.