You use fundamentally for emphasis when you are stating an opinion, or when you are making an important or general statement about something.
Fundamentally, women like him for his sensitivity and charming vulnerability.
从根本上说,女人们喜欢他是因为他细腻的感情和迷人的文弱气质。
You use fundamentally to indicate that something affects or relates to the deep, basic nature of something.
He disagreed fundamentally with the president's judgment.
他从根本上不同意总统的判断。
Environmentalists say the treaty is fundamentally flawed.
环境保护主义者称那个条约从根本上是有缺陷的。