For me, age is the big factor on why Sophie doesn't adopt some of the more trendier, funkier styles Zara often does. We are talking about a young, nubile woman in her early 20s compared to a woman in her late 30s with a young, infant daughter.
Secondly, as I recall Zara doesn't have a job per se but spends much of her time pursuing her equestrian hobby, which is a "job" unto itself, as well as attending some of the hottest, hippest parties in London and enjoying the city's night life. Sophie on the other hand, was a professional career woman who started her own public relations company and worked actively at that for many years, only within the last several years having left it to pursue her royal duties full time.
Thirdly, now when we see Sophie out and about it is largely in a professional setting. It wouldn't really be appropriate for Sophie to show up at a medical research centre in some of the outfits we've seen Zara in the past.
Fourthly, it likely just comes down to a matter of personal style and preference. Were Sophie Zara's age and in her position would she dress like Zara does? I tend to lean towards not; Sophie seems to prefer a more conservative, classic style in her choice of clothing. Much like Mette-Marit prefers a more streamlined, classic style to her sister-in-law Martha Louise whose style is much more bold and funkier, and the two women are about the same age and both of whom are young mothers.
And fifthly, I think that part of it does come down to their very different roles and obligations to the monarchy. Zara doesn't perform any royal duties on behalf of her grandmother, the Queen or in the name of the monarchy. But Sophie does represent the Crown when she attends various events and as such even how she dresses is part of this professionalism she maintains.
I don't see any point in asking why Sophie doesn't dress more like Zara any more than I see any point in wondering why Mette-Marit isn't more influenced by Martha Louise's style. Sophie has her own wonderful style that is separate from Zara's own unique style. We should just let each women be and delight in their special senses of styles.