TR-069 is standard from DSLForum to remotely manage networking devices. OMA-DM is standard from "Open Mobile Alliance' to manage smart phones remotely. Though the target market segment is different, I don't see any major difference between both of them as far as their functionality is concerned. I believe that both the standards are suitable for both kinds of market segments.
Similarities: Remote configuration and monitoring of devices TR-069 is meant for managing networking devices. OMA-DM is meant for managing Mobile devices. Firmware upgrade. HTTP based access - OMA-DM support other transports too. SSL for security. Both use XML for exchanging messages. Both support configuration parameters in hierarchical fashion (Tree form). Both expect devices to make connection to the central configuration server. Both support mutual authentication. Both have mechanism for central configuration server to notify devices of different events.
OMA-DM uses WAP-Push and SMS. TR-069 connects to device embedded HTTP Server.
I don't see many differences though. I will post new entry once I find more information.
Both of these standards have become very popular in their market segments and IMO both will be surviving for a long time.