One thing I can throw into the mix - Option 1 permits you to take advantage of TWOV transit without visa which would give you up to 144hrs in the greater Beijing area, and after HKG up to 144hrs in the greater Shanghai area, and eliminates the need to pony up for a multiple entry tourist visa - which for a US citizen is (I think) an expensive 10 year multiple entry visa. There's more detail and recent experiences in the China forum TWOV thread.

China 24, 72, and 144 hour Transit Without Visa ("TWOV") rules master thread

Whilst option 2 can do TWOV your entry is limited to 24hrs as you want to enter and leave in different TWOV regions.