As the question states, how does the size of the Death Star compare with the Yorktown space station featured in Star Trek Beyond?
This is a graphical depiction of how the two objects would look side-by-side, based on the best canonical evidence we have about their sizes.
According the the concept artist for Star Trek Beyond, Sean Hargreaves, the outer diameter of Yorktown Station is 40 miles.
Q. Do you remember how big Yorktown is supposed to be.
Sean Hargreaves: About 40 miles in diameter at the outer glass sphere.
By comparison, the canonical size of the Death Star (the first one) is 75 miles in diameter. The Second Death Star is 99 miles in diameter.
According to Sean Hargreaves, the designer of the Yorktown, each arm is intended to be 17.5 miles long and they open into the interior ball. This means the radius of the station is a little bit more than 17.5 miles or 28.16 km.
The death star, is said to have a diameter of 87 miles (DS1), or 99 miles(DS2). Both are significantly bigger than the Yorktown.
In fact, if you want to compare it in size to another Star Wars battlestation/large object, it's a bit bigger than the star forge, which has a radius of 25 km