I think the differences in the opening are about medium vs tone.

A book needs a great line to grab you. And this one starts with the most well-known phrase in Jane Austen's books. It is indeed comedic and lighthearted and yet it does state a truism about the times and the society in which these characters operated. Young men and women had to marry sometime and when someone as eligible as Mr. Bingley or Mr. Darcy comes to town -- well -- young women and their families naturally speculated about their chances.

Novels have time to set the tone. We look for them to grab us and pull us into the story and characters. We went from this statement to the introduction of the Bennett girls.

TV however has less time to grab our attention. By its nature people are also looking for that thing to grab our notice. What better way than to put two young, handsome, virile young men galloping on horseback in an English countryside to grab our notice? Right away we see Bingley, loud, friendly and deferring for advice to Mr. Darcy, his face somewhat hidden from the camera and Darcy already criticizing "country manners". We see action, vitality, Mr. Bingley's openness, Mr. Darcy's pride in a few minutes of action.

And then we see Elizabeth, watching them, intrigued by these handsome strangers and then skipping along a path. She's set up as curious, active and light-hearted without even saying a word.