What EM Does Well
It is relatively easy to dig up trivia and tidbits if you have a good enough archiving system and/or search engine. With biological memory, the information must be relatively significant to be remembered.
Directly related to the above: it is difficult to volitionally remember many things, whereas digging them up from an archive is easy.
Again, directly related to the above: information management is massively easier with pen and paper and libraries, not to speak of the digital realm. Furthermore, with the advent of ubiquitous connectivity, we can push the digital retrieval response times close to spontaneous recollection, which will no doubt produce interesting results.
That is, of course, unless things crash or break apart. But digital technologies enable us an increasingly available access to EM capacities, whereas biological mental capacities are available variantly.
Externalizing information works particularly well for tasks and other repetitive declarative information.
Directly related to task and information management.
This should be rather obvious; the biological mind cannot produce genuine randomness. A program can.
Once again, rather obvious: all rule-following is massively easier to an algorithm-driven program than to a human being.
This is only beginning to emerge, but we can do more and more together with the aid of EM technologies, whereas in biological connectivity, we are limited to very small groups.
Directly related to the above: real-time social networks are relatively small, whereas a digital network can consist of hundreds of active participants.
What EM Does Not Do Well
Machines do not as for now think creatively. Furthermore, while EM can augment creativity (think mind maps), it does not alone produce creative thought.
This is actually more relevant to AI than EM; it is also arguable that EM can be used to induce and direct emotions. But once again, it is a subtle interplay between the biological mind and EM.
It is very hard to think what would EM reflection even mean. Reflection is quite directly related to the biological mind, while of course it may involve EM components.
It seems metacognition is hard for both BM and EM. Perhaps a solution will emerge later? Thinking about thinking is not a very easy skill to learn, it appears.
Humor, analogies and irony
These require a human interpreter, and do not have an intrinsic EM dimension to them.
This is a field where EM will no doubt soon catch up. Nonetheless, right now automatic evaluation of information is still very elementary and gives a very varying mileage.