This answer really depends on the breed. Generally, beef cows produce much less than dairy cows do.
How much a beef cow gives depends on the breed, as well as individual cows. Most beef cows tend to give an average of 3/4 to 1-1/2 gallons of milk per day (or 10 to 20 pounds per day). Some breeds produce more milk than others. For instance, Simmental cows tend to produce more milk than most beef breeds (upwards of 30 to 40 pounds per day), whereas Hereford and Charolais are breeds known to not produce much milk, and are often called "poor milkers" by most producers. These two breeds tend to produce 10 pounds of milk per day or less. Other breeds such as Angus, and Shorthorns are considered more "moderate" milkers, in that they're milking capacity fits between "milky" breeds like Simmental (as well as Gelbvieh, Braunvieh, South Devon, and even British White) and poor-milking breeds like the aforementioned Hereford and Charolais.
As for dairy cows, milk production too depends on breed as well as individual cows, however these breeds are selectively bred to produce far more milk than their single calf can drink on a daily basis. Holsteins are the most well-known for producing the most milk, with daily milk production averaging around 60 to 70 pounds per day. (By comparison, a calf only needs 10 to 15 pounds of milk per day!)
Other dairy breeds have a daily milk production of:
The Bovine Practicum Q&A "blog" is an informative, just-for-fun section where I find a variety of questions that are often (and not-so-often) asked by inquisitive people like you, and answer them to the best of my ability. Much of the questions have come from a wide variety of reaches from the Internet.
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