There isn't an actual difference other than the fighting style and their place on the battlefield. Obviously, Sera with a bow, or Varric with Bianca will take a different approach to fighting than if you were to issue them with daggers.
Sera is also pretty awesome with a bow, even to the point where I might say I prefer her with it, and I have played my first Inquisitor as a Hunter who was taught with a bow, but switched to dual daggers during In Hushed Whispers. It fit my Inky, but Sera is more of a bow person to me. She even has, with some armors, specific archery gloves and protection. That she was displayed with in promotionals pre-release, by the way.
As for choosing at the beginning, you can choose whether you wish to start with a bow, or with daggers. In previous games, I can only speak for the City Elf and Human Noble, but your first weapon was always a Longsword, even if you wished to be an archer, or a two-hander... or anything, really. Now, you can choose what to start your journey out with, and you are also given one base ability from said tree. This would be Flank Attack or Twin Fangs (can't remember which) for Daggers, Shield Wall for Sword'N'Board, Long Shot for Archers, and I think Mighty Blow for Zweihänders.
You can of course switch later, as was the case with my Inky, Arianne, whom I mentioned starting with a bow, and then playing through the final two thirds of the story with her daggers, while (headcanonically) retaining her archery skills. I actually respecced her fully for Daggers once I got back from Redcliffe. (I planned for that armament switch, and In Hushed Whispers seemed like a perfect opportunity, as I had no melee in my two-person party of Dorian and Inky before you free the other two companions, who have been Sera and THE WALL for me)
Oh, and as Arcadia has mentioned... Sera is said to be "Quick with her bow" in Sera Was Never, which is a song dedicated to her. Varric could never unequip Bianca in DA2, making the auto-crossbow the only real choice in my eyes.