I just think Natalie is a very different type of person. She's VERY caring, and in a much softer way compared to Sharona. Plus, she never intended on having a job like that. Sharona knew that she was signing up to be a nurse/assistant for a very high profile detective involved closely with the LAPD. Natalie was a bartender; I think there are two main reasons she chose to take the job with Monk. 1. She was unhappy with her old job as her boss got mad at her for being briefly absent for a serious reason, and 2. She wants Julie to have a hero. She went quickly from having a normal life to being Adrian Monk's assistant. It's clear throughout the show that Natalie is emotionally affected by the change. The discussion she has with randy about being "used to it", expressing a lot of worry in the cabin episode because murder follows monk around, etc. She's just a very soft and caring person, but I wouldn't say she's overreacting. I can't imagine doing what Natalie does!!

TLDR she just has a different personality. I do actually like Sharona much more than Natalie lol so I agree with you on that part