They are almost equivalent; there's only a slight difference. When you use about to leave the emphasis is on that exact moment that you wanted to leave. For example: you put on your coat and walk towards the door to go outside. Then somebody asks "can you do the dishes?". The person replies "I was about to leave", because at that moment when the question was asked the person was already in the act of leaving, which is made clear by the coat that was put on and walking towards the door. When the person wanted to leave and then somebody asks "can you do the dishes?" the reply would be "I was going to leave" because the time between leaving and the question being asked is a little longer, and there were no signs like a coat. I hope it makes sense to you, because there's not a clear rule or such for this one :) Greets

'Was about to' implies that you were in the process of doing the action, but just before you did, you were interrupted. 'Was going to' implies that you were previously planning to do the action, but now it is doubtful that you actually will. The difference between the two is that 'was going to' hints at you not doing the action anymore, whereas 'was about to' implies that you still will.

My second sentence is wrong. I wanted to say " I was going to leave". Sorry!