Unless you received a separate manual or warrantee paper work for the actual tires on your vehicle, I'd recommend following the number on the door pillar.
There are so many tire and wheel combinations. Even if the manual covers a generic recommended PSI for the 15", 16", or 17" rims, MINI installs tires from several manufacturers.
The number printed on the label on the door pillar should match the actual options you spec the vehicle with more than the manual. The lead time and quantity that they need to keep costs down on a book also prevent it from always having the absolute most up to date information.
Those stickers, on the other hand, are filled in for your specific vehicle.
HTH,
Brant