When I was in a comedy troupe, we had a rule: "Never parody something that's already funny." Most of the time, it ends up being pale in comparison to the original. Of course, there exceptions to the rule, especially when the original wasn't that good to begin with.
(Example 1: if we did a knockoff of a SNL sketch where we "Need more Triangle!" you would just roll your eyes.)
(Example 2: We broke the rule once to parody Hans and Frans, casting them as Hansel and Gretel. It actually worked. "I'm Hansel... and I'm Gretel... And we're here to eat (clap) your house!")
I haven't seen either the SNL or the Animaniacs version but reading the one included here isn't too funny. A lot of a sketch like this is in the delivery. Reading it doesn't really get that across. Plus, you already pretty much know what's going to happen as soon as it starts. Oh well.
I don't mean to be ho-hum about it, I'm sure both versions are funny in their own right. But they'd probably be funnier if Abbott and Costello hadn't already done it so well first.