It is most unfortunate that it costs 4 euros to enter the cathedral (hint: if you are Catholic, just go to a mass) and another 4 euros to enter the Capilla Real. The cathedral is a nice example of baroque art, and it's bright interior is a nice contrast to the gothic cathedrals more common in Spain. It takes about half an hour to walk around and admire all of the altars. I did not opt for the audioguide, but in retrospect I'd probably recommend it. It's only two euros, and I imagine you'd get a lot more out of the visit.
The Capilla Real is the more interesting and unique of the two structures. An earlier building, it was built in the gothic style and houses the remains of the two Catholic monarchs, Isabel and Ferdinand (as well as their daughter Juana and her husband Felipe), two of the most important figures in Spanish history. Their lead coffins are visible below the floor of the cathedral, and impressive sculptures of the two couples lying in state are positioned in front of the altar. Next to the chapel in a nice collection of art which also includes some of Isabel and Ferdinand's possessions. Allow another 30-45 minutes for the capilla real. Note that the entrance to the capilla is on the right side of the cathedral (if facing it from the front).
Bottom line: If pressed for time, skip the cathedral and go for the chapel.
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