When you say full sun, do you mean afternoon or morning sun? I don't think either the azaleas or gardenias would appreciate afternoon sun. If morning then both should be fine and I'd recommend Gardenia jasminoides 'Radicans'.

Until a tree in the vicinity develops, it's mostly afternoon sun. Not ideal conditions, I know. However, spring & summer blooming (white) evergreen shrubs for this area are needed.

Whether for this particular area or not, white blooming azaleas will be a main feature of the property. Much of the area receives little sunlight (due to large oak trees).