The core Redirect has two problems, in my opinion.
First, it acts as a 404 collector. This means that every wrong URL which leads to a 404 error will result in an unpublished redirect being created. I understand the naive reasoning behind it, but in the real world this behavior ranges from daft to dangerous. The latter because the redirections table grows out of control with any database stability issues this might carry with it. This can be disable with some obscure setting, IIRC in the redirect plugin.
Second, the way it's implemented precludes certain types of URLs which do not result in a 404. For example, if you move an article to a subcategory the old URL is still valid and does result in the article being shown, due to the broken way Joomla! routing works. However, since this does not result into a 404 error the core redirect won't let you create a redirection from that old, obsolete URL to the new. As a result search engines will pick this up as duplicate content.
I tried to argue against this back in 2010 but it was like talking to a brick wall. So I spent all of a single afternoon to roll my own...
On top of that, Admin Tools' redirection can handle redirecting from non-SEF URLs and/or redirecting URLs with query string parameters (you can choose whether to keep or throw them away). The former is simply not supported in core (since it doesn't result in a 404 error) and the latter is also not supported in core since it merely strips all query string parameters. These last two features were added as a result of listening to user feedback. People made their case for such features, I saw a valid use case, I implemented them.
Overall, Admin Tools' Redirect URL feature is how it should be done, integrating user feedback. Joomla's Redirect component is a demonstration of how a developer who's never built a site and doesn't listen to his users would build a failed pile of warm, stinky, cow manure.
Nicholas K. Dionysopoulos
Lead Developer and Director
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