Please read entire spec before deciding which you should use!
For EBUS
Long Format: eg "[Mon] 09 Jun [2016] 02:15pm"
Short: eg "[Mon] 09 Jun [2016]"
For US
Long Format: eg "[Mon] Jun 09 [2016] 02:15pm"
Short: eg "[Mon] Jun 09 [2016]"
DOW and year is optional - see the Guideline below.
Guidelines
Use Long Format when time of day is important or when exact dates might need reporting to others (eg logs of actions, comments, or when an event might not reasonably be assumed to take place at midnight).
Use Ordinals "Today" to "Yesterday", when general recency is important (eg resources uploaded or applicants applied), then use Short form after that.
Use Fine-grained Ordinals for news items or similar "breaking" content. Use "Just now" to "23 hours ago" to "One day ago" to "Six days ago", then use Short format.
Usage day of week (DOW) and year Show DOW when a calendar week might also be a consideration (eg "Who is coming in on Monday?"). Show years only for the non-current year.
All other dates take Short format.
Rationale
Overall, we're trying for brevity (so no punctuation), immediate clarity (hence ordinals like "Today" and "2 hours ago") and allow for any international issues. We also think that 24 clock is too geeky, so willing to sacrifice a few pixels for am/pm.
NOTE: If location switching is going to be a problem, just use US format because people in the US are sensitive to these things. Whereas EBUS don't givvashit really.