As I mentioned yesterday, I spent a good chunk of the past weekend listening to the commentaries on the DVDs of Doctor Who Series Four. Listening to then Executive Producer Russel T. Davies talking over the two part series finale "The Stolen Earth" and "Journey's End", I was struck by the parallels between that apocalyptic storyline and DC Comics' seminal company wide crossover Crisis On Infinite Earths.
Davies talks repeatedly about how the story unifies the so-called "Doctor Who Universe," consisting of characters from the core seres, Torchwood and The Sarah Jane Adventures, in much the way that Crisis brought together all the characters in DC's comic book universe in one big story. The parallels go beyond that, however. There are references in the Who finale to the destruction of multiple alternate universes, similar to the destruction of the Multiverse in Crisis. Davros' master plan in "The Stolen Earth"/"Journey's End" to destroy all of reality, leaving only himself and the Daleks, bears a great deal of resemblance to main Crisis villain The Anti-Monitor's plan to destroy every parallel universe except his own. The Anti-Monitor even "steals" the Earth in the final issue of Crisis, dragging it into Qward, the anti-matter universe, in much the same way that Davros and the Daleks spirit the planet away to the Medusa Cascade.
After all, by his own admission, Russell T. Davies, who wrote the episodes in question, is not unfamiliar with American super-hero comics. In the commentary for "The Stolen Earth," he reveals that Captain Jack's last name was inspired by Agatha Harkness, the aged sorceress who was nanny to Franklin Richards in The Fantastic Four and mentor to the Scarlet Witch. She is, he claims, one of his favorite characters.
If Davies is enough of a geek to even know who Agatha Harkness is, much less to claim her as a favorite character, then it is perfectly reasonable to assume that he is at least aware of the existence of Crisis On Infinite Earths. From there, its not a huge leap of logic to surmise that he may have actually read the series and been so impressed by it that he wanted to write his own version of it.