Separating your publications into journals vs. conference/workshop
I happen to prefer a chronological listing. But it is really up to you. For example, if you work regularly in two different research areas you could even list publications and such separately for the two areas. 

The chronological listing makes it easier, IMO, to follow a thread or trend in research where other divisions don't. 

But, if you have access to examples of how others do it in your field it would probably be best to follow along. 

You are asking here for what amounts to opinion and those opinions may not be valid in your field. Do what is expected, I think.