
In a piece called "Old? Me? The Politics of Aging", screenwriter, playwright and lyricist Sherman Yellen wrote this a few days ago :

"Elizabeth Taylor and I share the same birth-date and birth year. She's been married seven, eight times and lived an extraordinary life, famous lovers, world-wide scandals, adventures, diamonds, Oscars. I've only been married once - most of my adventures were part of a splendid and tumultuous inner journey and I didn't make headlines or fortunes along the way. We share the same sign, the same chart, but oh, what a difference in our lives. So much for astrology."

Their natal charts are very similar, although minus rising sign and exact Moon position, both of which depend on exact time of birth - a whole lot of wiggle room remains. The two omissions are vitally important parts of any astrological chart.
There are millions, nay billions, of people being born on exactly the same date, same geographical location (or near enough) and leading totally different existences. That's life. Each individual uses his/her potential in millions and billions of different ways.

"So much for astrology" ?
Plant two seeds out of the same packet in a patch of garden - one might grow tall, bloom well and long, seed plentifully, while the other, a few feet away, but in the shade of a large bush wouldn't fare as well, or may grow tall but fail to flower as profusely, or perhaps a neighbour's dog came along and dug up a few of its roots, or an infestation of ants spoiled its growth or.....a million and one things can happen to a seed, a plant and a person. What doesn't change though, is the inbuilt potential of a seed, or a person, to develop in certain ways.

Back to those important astrological differences which are present even when two are born on the same day. Exact time of birth is paramount. This piece of information would, unless both were born within the same few minutes, change things fairly dramatically chart-wise. Rising sign would be different for each, which means the way the world sees each of them and the way each sees the world would be quite different.
Mr. Yellen may or may not have been using a bit of journalistic licence when he stated that his birthdate and that of Liz Taylor were one and the same, but even if he genuinely believed they shared a birthday, his comment, "So much for astrology" was seriously misguided.