I also propose that we stop separating the two and we look at how they are similar. All advertising and all marketing serves one purpose; to drive sales or revenue growth. No company is altruistic and spends money for the same of bettering someone else. That does not mean they are selfish, it simply means they are doing what they are supposed to do.
The difference between the two is whether the response you are measuring is direct or indirect. If you can track a response in a short period of time, or in an immediate period of time, then you fit in the DR bucket. If you require time and some additional inputs to measure a delayed or latent action, then you fit into the branding category.
I started calling in Brand Response back in 1998 and people latched onto the term. I like it still and it still satisfies a need.
Try to evaluate your campaigns against all of the metrics listed above and see what you come up with.