Hi Spring,
Let me give you an impression of how the sentences sound (in other words, of course) to a native speaker. as though they believed they were uttered by another native speaker:
1) As written, both sentences convey the same broad meaning, but with different nuances. Essentially, the meaning is exactly the same as sentence 2, because "as" in the first sentence takes the sense of "because". In spoken speech the emphasis occurs on the word "sometimes". The comma is wrong. Take no prisoners here - the comma does not reflect spoken English, and so it is wrong. It would be correct only if there were a comma after "that", making a parenthetic phrase. But such a parenthetic phrase is also wrong stylistically. A major problem here is that the placing of "only" distorts the meaning of sentence 1. In order to mimic sentence 2, the subclause should read "she gets distracted only sometimes." She still gets distracted, but "only sometimes", which we take to mean "less often". This is the same as saying "her ability to ignore distractions" (ie "not be distracted") has increased.
2) The listener becomes bored. This is one reason why passive voice is discouraged. To be correct, by the way, you must surround the parenthetic phrase "with the improvement of her listening skills" with commas. Notice how shorter and clearer sentence 1 is compared with sentence 2.
This is the best sentence:
"She reflected that she gets distracted less often as her listening skills improve."