Honestly, all my characters would get along just fine for the most part. I always have them do whatever I would actually do. There isn't a whole lot of variety in their personalities. The only real issue I think would crop up would be their views of the Chantry and the Circle. All of my characters are pro-mage, but my qunari inquisitor is gonna be a bit less forgiving and more resolved in that respect.
My Hawke is somewhat torn. Neither the templars or the Chantry seem to be entirely in the right or wrong. He can see an obvious injustice in the Circle but has seen plenty of mages commit awful acts through magic, losing control time and again. Meeting Corypheus sure didn't help things, and neither did losing his mother or having Anders blow up the Chantry. He lived his whole life standing by his sister, and has since fallen for Merrill. He continues to stand by his beliefs that magic is not evil in and of itself for them, but he can see all too well that magic can be dangerous and must be carefully managed. Magic clearly carries with it a greater risk than he once realized. It's all just a bad situation, and his will wavers at times. His belief in the Maker is shaky, and he seeks answers not really standing by either side in the war too firmly.
My Inquisitor will see the Chantry as wrong, not believing in the Maker or wanting to hear anything about "he who does not exist." She will also reject the Circle. To her the templars are hypocritical and oppressive. The mages they lord over are caged and repressed to such an extent that suffering is born not only to them but to those around them because they are either misinformed or just downright ignorant about their own inborn abilities. This might concern my Hawke, since her views may be too close to Anders'. To her, all the supposed "dangers" of magic are simply the result of ignorance. How can one wield a tool or weapon they do not understand without getting hurt? For her, the whole war is foolish. How can everyone project their fear over the act of one mage onto them all? Of course, the mages are a tragedy in and of themselves, ignorant for their lack of experience in the world. They hunger for freedom, but don't really know how to obtain it. They're all fools. I should note that she isn't as extreme as Anders even if she comes off that way.