Purpose, content, archiving strategies and access vary greatly, but depending on your purposes specific archives may have more relevant data to offer than others.
Furthermore, it is often interesting to see search results in different archives, where one may often find copies from different dates and of different quality to those already found in other archives. This of course is due to variations in both archiving strategies and technologies.
One example of interest is The Library of Congress's web archive section: https://www.loc.gov/web-archives/
It contains well curated thematic and event-based collections that can be extremely helpful if one is looking into one of the subjecrs represented here, and it may also serve as a showcase of cleaned and well ordered data collections.
For a comprehensive list of archiving initiatives and their different purposes and approaches one may consult Wikipedia's List of Web archiving initiatives.