BA Economics is an undergraduate course for 3 years training students in analyzing concepts by teaching them definition, nature and scope of economics.

BA Business Economics is also a 3 year undergraduate programme mostly inclined towards Applied Economics.

If you are more inclined towards business or you have some family business to carry on then it's beneficial to take Business Economics as it is more practical and you will learn how to apply the theoretical economics in the real world.

Instead if you are fasnicated with the academic nature of economics then opt for BA(Hons) Economics as it is more inclined towards the core of the economics.

Hope this helps.