Both locations are safe.

If you have to catch a very early flight, consider the Moxy near BER. (It's over a mile from BER, but as the crazy European I am, I've actually walked to/from BER at night. There's also a public bus and taxis aren't that expensive, either.) A Steigenberger a bit more expensive than the Moxy is right next to the airport. I've been to the Moxy, it's all right, never stayed at the Steigenberger.

The trains to BER via Ostbahnhof/Ostkreuz can be quite unreliable during the day which makes me think staying near BER may be the safer bet. But I very rarely, if ever, fly out of Berlin early in the morning so others may have better info on that.