Here are some details regarding both of them:
Toolbox
Pros:
- Was built after Polymer team started focusing on app side of Polymer
rather than elements
- Gets more updates than PSK
- Has all the other required tools (server, linter, bower, tester)
built-in
- In case of building an element (like to publish) it uses flat import
structure, where even though
bower downloads are kept in
bower_components folder and element to be made is kept outside the
bower_components folder imports are still made as though both are
present in bower_components
- Is made specifically to help developers in building their
application/element
- Is more in line with Progressive Web app vision of the team.
Cons:
Still in beta phase just like all the app-elements it uses internally
PSK
PSK was built with the purpose of providing a starting point for the developers who are new to Polymer and are more in learning phase. It has some pre-built elements with hard-coded data. If you look inside index.html you will find <template is="dom-bind"> being used which Polymer team recommends not to use in production environment. It was built when Polymer team was still focusing more on the elements side of Polymer as a result it does not use any of the Polymer's app-elements using which Polymer team has built the shop demo. A newer version has not been released since March as team is currently working on version 2 of PSK.