New companions is one thing I am very much in favor of. I know some people have Dorian pegged as someone who'll be returning to the roster regardless of who we play as, but I expect him to play more of a prominent NPC role.
I was fine with them bringing Oghren over from DAO to DAA; he was one of my favorite companions, didn't get a whole lot of screen time compared to everyone else for most people(I always went to Orzamar after dealing with the Circle just to grab him). But then they brought him in and undid what character development he did have in DAO and reset his approval to half way despite the fact that he was my Warden's best friend.
But, sure, ok. Rampant alcoholism is a chronic problem so Oghren regressing a bit is understandable and it all works out more or less for the best in DAA.
Then DA2 comes around. Isabela and Merrill I kind of forgive. I think there are issues with both of them; Isabela became a bit of an exaggerated caricature of what few traits she had in DAO, though there's some depth underneath that and some growth to be had. Merrill may as well have been a completely different character for what they did with her - she didn't have much personality in DAO but she definitely wasn't ...Merrill. But they wanted to expand on the Eluvian thing, so they tied that in. Still, I ultimately enjoyed both of their characters, but the fact that they share the names and backstories of minor npc's that appeared in DAO is largely incidental.
But of course the elephant in the room would be Anders/Justice. Which... yeah, not a fan of that. Didn't hate it as much as some people, and I still appreciate Anders and a bit of what he brought to the table. But damn.
Then we go to Varric. Like most people I rather liked Varric in DA2. I didn't care for him much at all in DAI. He was there to say "red lyrium is bad", and to call Hawke in so that he and Hawke can tell you the same thing; that Corypheus can apparently come back from the dead. Also to establish that every problem you had with DA2 was just the result of his writing. Aside from that he just complains and complains and complains.
Oh, and his quest introduces Bianca Davri, who is my most hated character in the series thus far because she's just awful.
So, in summary, I haven't seen an example where a carry-over character being a companion, or a companion getting two games, has worked out for the best; at best it's been incidental. At worst they missed everything that was likable about the character in the first place. Oh, and this is just me taking the game mechanics too seriously, but it always bugs me when a character gets de-leveled so they can be a companion in the next installment. Anders should not have regressed from a level 30 demigod to a level...four, I think, in six month's time. I'll give Varric some slack assuming he was lazy and didn't keep up with the marksmanship for the three years after the battle of the gallows, but Anders had no excuse.
So I want to see a whole new cast of companions with any returning companions being relegated to NPC status. I want to see a whole new cast of personalities, I want to see a whole new set of backgrounds and perspectives. I want to see character types we haven't seen before, I want to see romances they haven't told before.
And that's part of the reason I don't want the Inquisitor to come back, as I touched on earlier. Mass Effect proved that they can't do satisfying relationships over the course of multiple games without the LI being companions throughout. ME1 LI's got treated abysmally in ME2 unless they were Liara with LotSB installed. ME2 LI's got handled terribly in ME3 except for Garrus and Tali, who were squadmates. The rest were horrible, even with Citadel, except arguably Thane(the one who died) for his death and funeral being so touching.
So I don't want a situation where the Inquisitor's LI's get the DAA treatment of sending a letter and that's all you hear from them. And I don't want the ME treatment of one cutscene that amounts to nothing. And I don't want them tagging along, eating up companion slots, romance slots, and disk space with their audio files.