- No other animal is as tall as a/the giraffe.
- A/The Inland Taipan's venom is the most venomous one in the world.
I agree with Gustavo that "the" is the better choice in those sentences and others like them. I do have a problem with (2), though. Did you mean to say that its venom is the most poisonous venom in the world?
It doesn't make sense, except perhaps as a (weak) joke, to say that a particular animal's venom is the most venomous venom in the world. It's kind of like saying that a particular kind of juice is the juiciest juice there is.
Regarding (1), the indefinite article could be said to give a different meaning. Suppose dinosaurs still existed and you had a particular one in mind. You might say that no other animal (besides that dinosaur) is as tall as a giraffe.
(A) No other animal (besides the blue whale) is as big as a 747 jet airplane.*
But if we assume that "other" takes "giraffe" as its antecedent in (1), as seems likely in our contextual vacuum, then "the" is better. The sentence means: "The giraffe is the tallest animal in the world."
*footnote: I just made that up for grammar's sake. I have no idea whether a blue whale typically reaches the size of a 747. I wouldn't be surprised if blue whales tend to be even bigger than 747s.