I was on the inbound (the broken airplane, at least I think), HKG-->BKK. We kept the smaller portion of the boarding pass for that leg. This was EK385 on 11SEPT.

I continued BKK-->DXB on EK375 on 13SEPT, and, indeed, we kept the larger portion of the boarding pass for that leg. Same as the OP.

It seems that it depends on the airport, although I heard a rumor a while back that soon passengers would keep the larger section. After all, that's the only portion with GOLD written on it.

(The broken aircraft had no potable water dispensers, the captain told us a valve was stuck somewhere and everyone had to deplane to get it unstuck. Glad I was headed to the hotel.)