Question: if Cullen is a companion, how should he be differentiated from Cassandra in personality and story arc?
There is, I suppose, one starting point: Cassandra's backstory involved seeing good things from both sides, while Cullen has, for the most part, only seen bad things.
Tbh, I'm not sure. I think that's probably the reason why it's unlikely that Cullen would be a companion.
I guess he's got the added difference of having met (and in some cases known) the Warden and Hawke personally, which is at least a tiny difference in their general story, and like you said there's the bad side of things that he's experienced which differs slightly to Cassandra's story. That aside, at present I don't think there is much. I can only presume that perhaps his writer gave him a drastically different pre-DAO past and/or had something crazy/notable happen to him between DA2 and DAI to ensure that both character's personality/story arc is uniquely different from each other.
... Unless they want them to be alike, so that they "bond" and romance each other if the Inquisitor doesn't snap either of them up?