An industrial printing press can churn out many more copies of a text than an office copying machine. A drawing made by etching lines in the sand is likely to be erased before anybody could have photographed or otherwise reproduced it. In these general characteristics, memes are similar to genes and to other replicators, such as computer viruses or crystals. The genetic metaphor for cultural transmission is limited, though. For genes to be transmitted, you need a generation.
Memes only take minutes to replicate, and thus have potentially much higher fecundity.
On the other hand, the copying-fidelity of memes is in general much lower. If a story is spread by being told from person to person, the final version will be very different from the original one. That makes it difficult to analyse or delimit memes. This does not imply that meme evolution cannot be accurately modeled, though. After all, genetics was a well-established science long before the precise DNA structure of genes was discovered.