Blue Hawke, for me, was the tragic one. I like him least, he wanted to save everything, to compromise in everything and wanted to comply with everyone (the opportunist). At the end, he lost everything (faith, his friend, himself, what for he fought), but saved his brother... In my head their relationship ruined. (Perhaps, I should try another one, in a different path...)
Purple Hawke's not really always fun, and not really cheerful. Depends on the mix, he can be a funny, charming but nice guy, or a burned out sarcastic bastard, or a serious sociopath too. The sad clown. Probably my favourite, with red!Hawke.
Red Hawke can be the most trustworthy wo/man ever. Can't lie, and manipulate. His/her moral standards are high and cruelly honest. A true knight, a hero, but not the kind one (true, can be, if feels). Hothead but the best loyal friend ever. Or a cold-blooded killer psychopath – this one can be manipulative as well...
Or a mix of these – depending on your imagination.
I don't agree, that the three base personalities make Hawke less flexibile than the Warden or especially the lukewarm Inquisitor.
Hawke has the main personality, but you don't need to insist always to this (in fact, much better if you don't insist to Hawke's main colour always).
A nice man able to lose his patience, a jokester not always funny, and a quick-tempered, loud man can have soft, quiet moments.
Mixing these traits gives believable personality to Hawke.
And for example, in many times, the red answers pro-Templar, pro-Circle answers, but my every Hawke's pro-freedom. My red Hawke a radical, "no compromise" one, he would never agree with the necessity of the Circle. (he chose the blood magic especially because against the Templars.) If I would use always the red answers, he wouldn't consistent.
So no, I must mix the answers, if I want a consistent, living character.
And purple Hawke can be a charming, humorous guy, who sometimes hothead, but nice. And can be a burned out rude-sarcastic bastard. Or when the game begins, rather the first, but later more and more the second.
Red Hawke can be righteously angry, hot-head, but the most trustworthy person ever. And can be a cold-blooded psychopath...
Or as mine: a man with some anger-management problems, and with rude humour and social problems. But not that bad, as he seems and want to show himself. Can be surprisingly merciful.
He's probably my favourite now, with my purple/red reaver/berserker.
Both with Anders, and both are great with him.
@Kalen Boies
I agree, that red!Hawke is pretty with Anders, but a pro-freedom red!Hawke is a real power couple! In friendship.