It would technically be a 408 Timeout. There are two types, time out before provisional response (100/18X) or after provisional response, A 603 means the other side did not want the call or could not accept the call and there are not other options like voicemail or CF for it to use.
The reason that I asked which side was sending the 603 is because the PBX would most likely send a 603 back to the provider when the other channel (phone) sends back a 408. There are two sides to this call and Asterisk is taking the response from the phone, processing it and present a response back to the original caller channel.