To quote from Engaging anthropology: the case for a public presence By Thomas Hylland Eriksen
Anthropologists have noted, with some irritation that none of the leading advocates of memetics discuss earlier work on cultural diffusion, which is very considerable.
The accusation is probably correct. So, a few brief words from me about cultural diffusion.
First a couple of popular articles on the subject - to provide some context:
http://en.wikipedia.org/wiki/Diffusion_of_innovations
http://en.wikipedia.org/wiki/Trans-cultural_diffusion
To a certain extent, the issue is one of terminology.
Memetics replaces the concept of cultural diffusion with cultural epidemiology - the idea that ideas spread contagiously - like mind viruses - and that epidemiology is a more appropriate metaphor than diffusion was.
On the positive side, terminology based on epidemiology captures the ideas of cultural immunity, vectors, resistance, rapid evolution and pathogenic infections well. On the other hand, it is hard to spell, and tends to suggest ideas are more pathogenic than they are beneficial symbionts - which is not necessarily accurate.
Diffusion tends to conjur up the idea of physical diffusion processes (such as gas diffusion) more. It fails to capture the dynamic, biological side of the process. There is no hint that the ideas might evolve. On a more positive note, it is more neutral about whether the culture is beneficial or harmful to the DNA it coexists with.
I don't think there is much of a contest really. The memetics terminology is much better. The anthropological terminology seems to have been largely abandoned by anthropologists since then as well.
So: the idea of cultural diffusion was a rather weak one - let it die off naturally.

