Hi Garnata. Never been to Farne Island but I can tell you the Isle of May is amazing. You will get point blank views of nesting puffins, eider, razorbill, guilliemot, fulmar, kittiwake, shag, common tern, seals, and on the boat trip you should see loads of gannet.
Other places in the area are the Bass Rock, (world's largest single island gannet colony), with puffins on the small islands just off North Berwick. The boat doesn't land though.
Also in the area is St Abb's Head national nature reserve. All the same species as the Isle of May but minus the puffins. On the upside you have a good chance of peregrine and raven. The cliffs around the lighthouse have the most birds and the best views. Also St Abbs is on the mainland and therefore not subject to heavy seas that can mean baot trips can get cancelled.
Good luck, I'm sure you will enjoy all of the locations you visit and get lots of good pictures.
Mark