The First Problem of the Week

Hey Everyone, we decided that it would be fun to do a problem of the week type thing, so here is the first of many to come. Leave your answer in the comments and check back in a week for the answer.

Alice and Bob own roughly rectangular pieces of land on Earth, which is assumed to be a perfect sphere of radius 3950 miles. Alice's land is bounded by four fences, two of which run in an exact north-south direction and two of which run in an exact east-west direction. Her north-south fences are exactly 10 miles long; her east-west fences are exactly 20 miles long. Bob's land is similarly bounded by four fences, but his north-south fences are 20 miles long and his east-west fences are 10 miles long. Whose land has the greater area?

Source: Due to Lester R. Ford, an avid problemist who was editor of the American Mathematical Monthly during World War II and, later, president of the Mathematical Association of America.