Whenever there’s changes to the story we know, thousands of sharp minds get involved in the speculation game. Why did they change that? Here’s some of the best answers that have come in.
Tengwar wondered who we saw battling Lurtz in the trailer – Aragorn or Boromir? He makes a strong case for the former:

“This is just a guess, but I would bet my bottom dollar I’m right. Lurtz is going to kill Boromir and then Aragorn is going to kill Lurtz — a’ la Qui-Gon being killed by Darth Maul who is in turn killed by Obi Wan. Not that I’m suggesting that’s where they got the idea, but think about it: They have to end this movie on some sort of victory. They can’t make it all the way to Helm’s Deep [in the first movie] like Bakshi did so they created a character Lurtz who could be a villain Aragorn could kill. They couldn’t use Ugluk because they need him for the The Two Towers. This would be the only reason to make up a new character (ie to kill him as a climax to this film). I’ll bet you a hundred bucsk I’m right about this. It makes perfect sense. When I thought about it, it soothed my anger about Jackson creating a new character for this movie. It’s necessary because Fellowship ends so anti-climatctically. “

As for the Sword that Wasn’t Broken that Strider wields on Weathertop, Nick Friend agreed that Strider would need to carry a usable weapon for normal foes (why a sword, though?) but he also said something else very interesting:

“It occurs to me that Aragorn’s decision to carry no sword but broken Narsil is symbolic more than anything else. He is an incomplete man, as it is an incomplete weapon. When he is revealed as the heir toIsildur and is prepared to make open war against the East, he knows it’s time to reforge the sword and carry it whole for the first time. It’s a bit of chivalric posturing, much like the English knights of the 14th century who would put on an eyepatch before leaving on campaign (even though they had two very good eyes), while taking a vow not to remove it until they had done some deed of valour dedicated to their lady. Or something like that.”