This trial is conducted in Europe and the United States of America (USA). The aim of this trial is to compare the effect on glycaemic control of liraglutide or exenatide when added to subject's ongoing OAD (oral anti-diabetic drug) treatment of either metformin, sulphonylurea or a combination of both in subjects with type 2 diabetes. Two trial periods: A 26 week randomised, followed by a 52 week extension (14 + 38 weeks) where all subjects received liraglutide + OAD after previous randomisation to either liraglutide or exenatide, both combined with OAD treatment.