A first step is determining what you want...i.e. a complete Desktop environment with X11 and a graphical web browser?
[ttylinux] provides a complete command line environment and is ready for Internet access.
Forget this, then.
Comparing the other three via their Wikipedia entries, I'd first drop Feather Linux as it seems dormant.
Then see this note on DSL's page:(1)
Due to infighting among the project's originators and main developers, DSL development seems to be at a standstill, and the future of the project is uncertain, much to the dismay of many of the users.
By exclusion and from these four, I'd end up with Tiny Core (or maybe Micro Core without the graphical desktop but then you need another reason to exclude ttylinux). Also note that their core concepts are interesting and probably differ from one is used to with other distributions.
Of course, many general-purpose distributions can probably be trimmed down to be resource-friendly, so Debian (especially Emdebian) (or Arch) could be a winner, too. (Not to mention non-Linux OSes, e.g. {Net,Free,Open}BSD)
(1) Edit: DSL "is once again being actively developed" (as an anonymous edit request pointed out)