As a host:
I always try to find Sunbros, because I think of Sunbros as a Covenant specializing in PvE and co-op and they are usually very good and cooperative. They do whatever shizzle I come up with and usually don't care and do it very effectively anyway.
They give off the feeling of "Hey, let's go through this together."
White phantoms tend to do whatever they please, ignore host, rush for boss etc. If I want to search the whole location and pick up everything, Whites usually just go wherever they please, or try to make me hurry the f*ck up.
They also seem to be more prepared to PvP, so I usually see white phantoms as gankers. No offence.
They give off the feeling of "Ok, let's get this sh*t over with."
As an invader:
Sunbros usually try to protect the host, but don't care about me much otherwise. They usually stick to the host and either try to push me away or go together at me, to get rid of me.
Whites are more aggresive and will sometimes leave host alone and rush at me, as if they were waiting for me. In ganks, Whites are also more aggresive than Sunbros.
Sunbors seem better for questing and Whites for ganking.