Verified across browsers (Firefox & Chrome) and across platforms (OSX & Linux):
> Date.parse('2012-01-01')
1325376000000
> Date.parse('1/1/2012')
1325394000000
Relevant:
https://github.com/portablemind/compass_agile_enterprise/wiki/Javascript-Date.parse-bug%3F
The format 2012-01-01 is interpreted as ISO 8601 conformant, and the Z timezone (+00, Universal Time Coordinated) is implied. The format 1/1/2012, if accepted (this is implementation-dependent), is taken as local time.
To get more consistent results, use a library like Globalize.js.