Does the print version matter, or the card name?
According to this link, the old cards are still valid, but you must ensure that your opponent is aware that the effect has been errata'd and provide them with the new effect.


  If you are using an “Old Text” version of a card in your Deck, you must make it clear to your opponent that the effect of that paricular[sic] card is different to what you are currently playing.


With regards to the Slifer the Sky Dragon example, the original card was never legal to be used in a match, Errata or not. It is a promotional card that includes the explicit text "This card cannot be used in a Duel," and is distinct from the actual card that lacks this text and includes the card's actual effect text.

This can further be established by using that website's Card Database and searching for the card (result of the search). On that page, it shows all the legal sources for a given card. The first time the card became legal to play was in August of 2012 when it was distributed in an issue of Shonen Jump. By extension, this excludes the original versions that were released alongside the Gameboy games in the early 2000s.