Hiya tk, you old schizophreniac

Here's how I use the two, at least in terms of the issues tabs you can extrapolate to tasks and problems.
In general, when things arise that we dont have an answer to, that are related to elements not yet modelled (or modelled but not yet "published") that require either discussion with stakeholders or escalation through the project heirarchy, we add them as system issues. They are thus captured and can be handled at the next appropriate talkfest.
Note, we do not manage real issues (i.e. things that must be resolved beyond the modellers authority/responsibility level) through EA. We do, however use it as a means to quickly capture them for later transcription to the project/program issues register if necessary.
An example would be something like "We have not been able to get a signed off definition of the <product x> default pricing parameters from the marketing deopartment. This spec was promised as the definitive example for defining the default price structure parameters. Alphonso from marketing says they do not have such a document. This prevents us from completing the price rule logical design."
On the other hand element issues are specific to the model (diagram even), many of them are or will be resolved in the course of developing the solution design. As they are associated with the element concerned and can be included in the generated documentation we have found that they do not tend to "get lost" in the general project wash. In addition, by using the ctl-space element tagging feature, (the little red triangle) the user gets a memory jog every time they add the element to a model that "something is awry here".
I agree that the EA issues model leaves things to be desired in terms of an issues management system, even at the element level. I have started several times to build an extension add-in to give me the data, control, reporting etc that I "need" in this respect . Sadly, the real project keeps getting in the way of completing it! ... :-/
Bruce