I never noticed that, so I looked it up.

Here are the differences I found when comparing a BA-issued boarding pass for a BA flight with an AA-issued boarding pass for an AA flight (both obtained by an agent, not a kiosk or OLCI):

• AA does not print
  1. baggage info (the number of checked bags and their weight and number of unchecked bags) nor
  2. the check-in sequence number (which AA's systems don't use)
• BA does not print
  1. the PNR code (record locator),
  2. the e-ticket number,
  3. the nationality and last 3 digits of the passport used,
  4. the actual class booked (it replaces it with a generic cabin code), and
  5. the agent ID of the person who issued the boarding pass (i.e. checked you in)

All in all I think the AA boarding pass has much more information, and is more useful.