First off, I want to say that when I advocate below for point-systems, it's a general advocacy, and not meant for this tournament. I believe that this tournament should be winner-take all, because Nats are WTA, and more importantly because that's how the rules were laid out from the beginning.
Furthermore, I don't discuss how things ARE set up, because this is a discussion (at least the one I want to have) of how they SHOULD be set up, and the way things are has extremely little to no relevance on that.
Having said that:
The first big difference I see in points vs WTA is in what kind of play they promote. WTA encourages you to take risks, because all that matters is getting first place or not. Points encourages you to play some system which is less risky and more consistent. Note that you probably still ought to take SOME risks, as is inherent in all forms of dominion, and the direct amount of risks you take is dependent on which point system you select. On the surface, these are just two different things, with neither being straight better than the other. It's a preference thing. However, I have a strong preference for points, and let me explain why.
So there's the cliched treasure map example, which has so much baggage that I'm going to step away from it. Here's another example. Opening something like fortune teller/potion when the cheapest potion-cost card on the board is golem. Now, assuming the other player doesn't attack you or mess with you or anything (which may not be the best assumption given that there's an attack, but this is a concept that makes sense anyway), your probability of spiking a golem on your first reshuffle is a hair's breath over 1/3. This probably makes it totally worth it under a WTA format, assuming it's a deck where golem can help you out a lot. But on average, this is a play that actually HURTS your deck quality, hurts your position. I don't particularly like encouraging this, first of all, but let's dig a little deeper. If this really is worth it, then everyone does it, yes? I mean, if they're playing well, making the 'right' decisions, they're all going to do this, yeah? But the point is, you now all have marginal chances of making that hit. Most probably, one of you gets this advantage, and the other three are way behind, and there's a HUGE spin toward that one guy - not that the game is totally over, but he has a MUCH larger chance of winning - based solely on how the shuffle fell, right off the bat. Basically what I'm saying is that WTA promotes strategies where, on a larger number of boards, a small amount of luck makes a large amount of difference. And especially for competitive environments, I don't like that.
Second, there's the issue of the number of games you have to play to get clear results. This is the direct result of having more information carry over from the point system than WTA. If you play 8 4-player games, you don't have a great idea as to who the best players are by your WTA metric. Probably nobody has more than 4 wins, and because of the high variance from a single game, we don't have that great an idea that mr. 4-win or mr. 5-win is really the best guy. However, if you play points matches, you have a much better idea, because you have more data. Now, of course, if you think winning is the only thing that matters, you reject this assessment, because you don't think the points metrics are meaningful; and this is mostly a logistical issue, really. But my point is that if you accept metric A, WTA, you need more games for results to have the same stability you get in fewer games from metric B, a points-based system. Because A has a higher inherent coefficient of variation than B does.
Finally, there's the kingmaking stuff. Which gets its own post.