It's half-off on PSN this month and I was considering spending some of my (limited) cash on it. Is it worth ~$20 bucks?
Depends. Have you played Dishonored, it's DLCs and Dishonored 2?
If you have and you enjoyed those, then Death of the Outsider is basically a shorter and slightly shallower version. It has well-designed and detailed levels to play around in, although none of them are as good as the very best the other games had to offer. The new powers open up a nice array of interesting gameplay possibilities, but you get all of them early on and there's no getting new ones or upgrading them later on, aside from some Bone Charms which don't radically alter how you'll play. Character progression in general is more limited.
They also did away with the High/Low Chaos system, so you can do a pacifist ghost run, gleefully murder yourself through, or anything in between, and it will no longer have any effect the story outcome or the environment. That can be seen as a pro or a con, depending on your stance on morality systems. As for extra content beside the main campaign, there's an Original Game+ mode that lets you replay the campaign with Dishonored 2's powers and a Custom Difficulty with some 20 variables so you can tweak the game to your liking. Overall, I think it's pretty good and a fitting closing chapter to the series.
If you have played the other games and didn't enjoy them, then Death of the Outsider won't change your mind.
If you haven't played the other games, then I would say it's not the ideal starting point. The gameplay can be enjoyed regardless, but its story and events tie directly into those of the others, particularly Dishonored 2. It's more or less Dishonored 2.5, rather than a fully standalone game.