DL has invested millions in a fully real-time computer system they term the Delta Nervous System (Google it for more info), which ties together all of their systems--dispatch, maintenance, weather, reservations, SkyMiles, crew scheduling, etc.--into a system where every component knows everything that's going on as soon as it happens. One benefit of that is that the SkyMiles systems know virtually instantly when a customer boards a flight and can immediately post the miles to that customer's SkyMiles account.

Sending the data to AS is still done semi-manually (by FTPing a database file), but theoretically, the database file should contain records right up until it is sent. Therefore, if you fly a DL flight a couple of hours before the database is sent to AS, your flight could post to AS as soon as AS receives and processes it. For its own flights, AS has to wait until the older, slower Sabre system processes and sends the data to the Mileage Plan system (which seems to be taking longer to process stuff these days, despite the faster and more flexible computer platform). That's how a DL flight could post faster than an AS flight.