As a general answer, independent of Feedzirra: they are separate and serve different purposes. ID/GUID are per-item properties defined by the RSS and Atom specifications to identify feed items across fetches. When you fetch a feed again you can track which items you already received the previous time (e.g. Are RSS guids actually expected to be _globally_ unique?).
Etag/Last Modified are provided when you request a feed in order to identify the version of the feed that you already have and to avoid retrieving an unchanged copy (e.g. What is the point of If-Unmodified-Since/If-Modified-Since? Aren't they superseded by ETags?).
You should use both.