It's an analogy, but not all analogies are metaphors (or similes either).
Someone saying this probably means that Australia Day has, for people of a particular subculture qualities that are indeed akin to those Christmas has for other people.
Now, this might be a bit of a stretch but that makes the analogy hyperbole but still a direct analogy rather than a metaphor.
To be a metaphor or simile it would have to make the analogy not with another day or recurring event like Christmas, but with something completely different:
"Australia Day is like Bert Newton's hair: Festive, but best not to analyze too closely lest you see the truth."
That's a simile because holidays and people's hair are not of the same class of thing at all. If it had been "Australia day is Bert Newton's hair" (rather than "is like") then it would have been a metaphor.
As a rule, metaphors are rhetorically stronger than similes, because they make a more direct claim (consider the impact of Shakespeare's classic "All the world's a stage" to if he'd said "All the world's like a stage" or "All the world is as a stage" it would have been a simile), but for the same reason similes can work better when the analogy is a greater stretch, and especially if you need to explain the analogy (as in the tweet quoted above).