True Believers - the ones who favour the David Attenborough approach - will say things like "The characters in my stories are real people to me - they have their own agendas and I can't make them do anything they don't want to do." Meanwhile, Architects regard characters as simply part of the overall construction; to them, treating their characters as sacred makes no more sense than saying mortar is more special than bricks when it comes to building a house. And of course, both camps strive for 'characters that feel real in their stories; that their readers can connect with - even if they don't particularly like them.
But it can all go horribly pear-shaped too. No matter whether you believe your characters are semi-sentient beings living inside your story-brain or the building blocks of your story-sculpture, sometimes they just won't do what you want them to do. They throw their toys out of the pram, the pieces won't fit together properly... pick your poison, the end result is the same. You find yourself saying some variation of "She won't do this anymore! I needed her to do this thing but now I can't make it work and I don't know what to dooo!"
How can this have happened? How can people that were made by you, in your own head, suddenly turn around and do a Kanye West on you with the plot you carefully and lovingly constructed for them? And more importantly, what's the solution? Do you treat them like real-life rock stars and bend over backwards to please them - the natural instinct of the True Believer? Or do you, as the Architect, get your own Inner Kanye on and decide that, actually, you are the God around here and you decide what goes down?
If you're a True Believer, you're faced with two options. Option One is to find someone else to carry out the part of the plot your troublesome diva character won't, or change your plot to fit in with what said diva 'wants' to do instead. This may still require at least some plot tinkering, because even once you've found your willing backup character, if he wasn't around for that moment originally you'll have to engineer some way to put him there now, that makes sense and doesn't muck things up for other characters or plot points ("but he can't be rescuing Mildred's cat from the burning building - he's supposed to be bonking Pedro's wife in a grungy motel two hundred miles away!")
If that's not possible, you're left with option two - and that's not automatically a bad thing. You might only have to tweak things a bit, so that you change a few events but everything still basically heads in the same direction. You might even find you like the new ideas much better than the old ones. But sometimes the changes you have to make are so radical that it means you're now telling a different story from the one you set out to tell. And that's fine - as long as you're more emotionally invested in your characters than the story they're enacting for you. But if the original story was one that was dear to your heart - that made a point that your storyteller soul felt driven to put out into the world - and now that message has been sacrificed for the 'integrity' of your characters... well, it might be difficult to tell the new story with the same passion. Especially if a part of you is still grieving for the loss of the old one...
By now the Architects will be facepalming at the whole touchy-feeliness of the above and crying "Oh for god's sake, get a grip!" Since they view their stories and their characters like an infinitely-supplied box of LEGO, their attitude is that they built this world and the characters in it, and if some of them bricks aint doing what they oughtta they're gonna get a smiting from the all-business Hand of Story God. Characters and plots can be broken apart just as easily and efficiently as they were made, and then rebuilt into whatever serves the story they're determined to tell. Hermione's phobia of clowns means she won't date Frank, the Ronald McDonald mascot at her local fast-food joint? Pffft, get rid of her phobia then. Or have Frank flipping burgers instead. No biggie - as far as an Architect's concerned, making it all work together is surgery, not psychiatry. No mourning the demise of the Story From Their Soul for them...
What they have to watch out for though, is that they don't allow this single-minded approach to blinker them. While it's certainly possible to 'change' a character to fit the story by removing certain personality traits and replacing them with more suitable ones, Architects need to be sure they're not doing so purely through stubborn determination to make that character fit no matter what. Because if it's done badly or with poor judgement, you get the Frankenstein's monster effect where it looks like a character has been randomly bolted together from a mix of different kits, just so that it will behave the way it 'should' at any given moment.
And this is why character biographies are a writer's best friend - whether you're a True Believer or an Architect. Sometimes just tinkering with one key event in a character's backstory can be enough to change their personality completely, believably - and, crucially - in ways that better fit their role in your story ("Mungo always felt inferior to his older brother, who was lauded as 'the smart one.' What if Mungo was the smart one instead, and felt that his brother resented him for it?") You can go as deep as you feel you need to; some writers approach it in the same way as a therapist might profile one of their long-term patients, while others include even the teeny-weeny tidbits like favourite colours, tv shows and ice-cream flavour. (Personally I feel the latter is where you can potentially cross the line from Useful Knowledge to Pointless Time-sink, unless knowing that level of trivia actually plays some crucial part in the story. But hey, if it ices your gateaux, have at it...)
So... which are you? Are you firmly one or the other, a bit of both - or do you flip between the two depending on what you're writing? (I'm probably more inclined to the last one.) How do you deal with the challenges of 'unruly' characters? I'd love to know.