Shaped by Circumstances

From how Katherine has been acting recently, it seems like she has given up on opposing Petruchio. Since it is in her best interest to go along with what he says, I think that she will outwardly appear to be tamed. For all intents and purposes, she'll be tamed and look like a new woman, but since she has such a strong personality, I suspect that she will covertly oppose Petruchio from time to time in ways that won't incite punishment from him. Since the strength of their personalities seem to be relatively equal, Petruchio has the advantage because he's the male in a Shakespearian marriage. Although Katherine might have a strong personality, it's much easier for her to go along with the taming so that she isn't ostracized by society or tormented by her husband.
On the other hand, since Bianca seemed to be showing some signs of independence and assertion (especially with "Cambio" and "Litio") and I think that she'll probably start to lessen the sweetness and submissiveness once she's married. I suspect that Katherine and Bianca are actually inherently not as different as they seem at first glance, it's just that Katherine had been conditioned over time to be a shrew by what people expect of her – Shakespeare wrote that she was famous throughout Padua for her scolding tongue. Similarly, Bianca had been submissive and sweet because that's what everyone expected from her – not to mention it made her life much easier than her sister's. Once she's married to a young man that she favors (she can basically get anyone she wants with her cloying attitude), she'll have more of an opportunity to drop, or at least lessen the dainty, girly facade. She seems to be the sort that would gradually stop being so sweet as she gets bored of her partner.
However, Katherine may actually end up being loyal to Petruchio over time (since he's the one who saved her from the "shrew" label) and he may gradually become less of a bossy, misogynistic rogue as they become more comfortable with each other. I think that Petruchio was just being over the top oppressive to "tame" Katherine and put on a show for the others in Padua. Once their reputation has been established, he can lessen the shrew tamer act and safely be more respectful of Katherine.

(Note:  Since I can't predict something I'd already read, I tried to remember what I thought before I'd read it, so much of this post is speculating about events past the ending of the book.)