Archive.today has a different approach to the baseline archive technology (executing javascript at archival time and saving the DOM instead of saving and replaying server responses verbatim). Additionally, Archive.today employs a number of site specific mitigations which aren't visible to the end user. In some cases, for instance, they use accounts, but then retroactively modify the DOM to mask this mitigation. [0] While the exact strategy they use for Twitter isn't known to me, they are doing something by their own admission. [1]

[0] https://blog.archive.today/post/708008224368001024/why-isnt-... compounded with personal observation.

[1] https://blog.archive.today/post/708565142782246912/pretty-pl...