The 'Dukes of Hazzard' star - who recently went from a blonde to brunette - was with her new musician boyfriend when he allegedly pointed to a picture of Ashlee on a magazine cover and asked "How old is this picture of you?"
Jessica is said to have lost her temper with John and insisted she and Ashlee look completely different.
A witness told
Though Jessica, 26, was once close to her 22-year-old sister, they have reportedly started to grow apart since Ashlee lost weight and dyed her hair blonde.
Ashlee is also said to have had a nose operation, although she has never confirmed going under the knife.
A source said: "Jessica hears the catty talk about how Ashlee looks like her - from two years ago. It totally bothers her.
"There's certainly a sibling rivalry between them."
Jessica recently said she is now comfortable with her figure and feels "beautiful" even when her weight fluctuates.
The star revealed: "I've really become comfortable in who I am and in my skin. I feel beautiful whether I am five pounds heavier or five pounds smaller.
"I'm actually a natural brunette. I was really blonde as a kid, but then I just started getting darker and darker."