Do they mean the same thing?

They mean the same thing, but A) makes the actions more important and B) menas her reaction to them more important.

Pretty much the same. 

Somewhat. But “A” kind of implies a physical contact.

A. "As she approached the kitchen, footsteps and angry shouts met her ears." means that "Her ears met footsteps and angry shout as she approached her kitchen."

B. "As she approached the kitchen, she could hear footsteps and angry shouts." means that "She heard footsteps and angry shouts as she approached her kitchen."

Both of those sentences would mean the same thing.

Yes, but one is way more poetic than the other.

Right. They mean the same thing.

A. Is a more prosaic way of saying this.

B. The way it is said in normal American English.