Why would you choose to spend the resource?

Bigger question is why would you choose to run this character.

In theory, the idea is that her special ability is meant to help you run a "mill deck" - that is, one that achieves victory through the game condition of your opponent's deck and hand being empty.

Practically speaking, that approach is hard to achieve anyway, and is much more efficiently achieved with discard effects, as discarding interrupts and interferes with an opponent's game plan while running down their deck. 

All in all, Padme is a bit of a weak card at time of Awakenings only. Future cards may make her worthwhile though.

Yes, but I was looking for a scenario where choosing to spend a resource is better than choosing to discard the top card of the opponent's deck. The only risk I see is if there was an ability that would cause the discard to fail.

I think the formatting might be confusing your understanding.  Formatted differently:

[Special] - Discard the top card of an opponent’s deck
OR
spend 1 resource to discard the top 2 cards of an opponent’s deck.

You have to spend 1 resource to place the top 2 cards of their play deck into their discard pile.  Otherwise, you only get 1 card.

You discard the top card of the deck, or pay to discard the top two. Not discard or pay to discard two.

Oh, now it all makes sense. I got it completely wrong at first. Thanks!

You're not the first person to parse that wrong - I've seen the same misunderstanding elsewhere.

English language is messy, eh?

I think part of the problem comes from reading FFG LCGs, where traditionally everything on the left side of "to" is a cost. That's not the case in Destiny, which doesn't have an RRG definition of "to". Instead, you just have to go with plain English, which is inherently messy.

I think part of the problem comes from reading FFG LCGs, where traditionally everything on the left side of "to" is a cost. That's not the case in Destiny, which doesn't have an RRG definition of "to". Instead, you just have to go with plain English, which is inherently messy.

Indeed. Coming from AGoT2 and WH40KC, I mindlessly parsed that as [cost] to [effect]. SWD wording is less rigorous. Also, in LCGs you always pay costs with stuff you control, which is not always the case with SWD (see Force Throw). Also, Hunker Down invites trouble with its effect that starts with "if", which I interpret as "when" and which should have been either "before" or "after". It doesn't matter much at the moment, but upcoming cards interacting with Hunker Down at about the same time its ability triggers would make things messy since it's unclear precisely when its ability triggers.