Mathworld has broader scope and a tighter license (http://mathworld.wolfram.com/about/faq.html#copyright)

LMFDB contains a large amount of extremely difficult to compute data about mathematical functions that arise in number theory, which took decades to compute and debug, and relations between that data. Just as hundreds of gigabytes of detailed astronomical data is not in Wikipedia or Wolfram Mathworld, this data about number theory is not in Wikipedia or Wolfram Mathworld either, and it never will be.

I should add that behind the scenes LMFDB really is a (MongoDB) database, there's an API that @hasch (here on HN) wrote, so that data can be recovered in JSON format, etc. To give some sense of what is in there, this http://johncremona.github.io/ecdata/ is just a tiny bit of what is in LMFDB.

LMFDB is more specialized. But given an infinite amount of time, the others would acquire that information.