This card is insane, let's get down to it.
From the corp's perspective, you have to spend a click to install Prisec, then 2 when the runner accesses it. By contrast the runner spends 3 creds to trash it, then 2 creds and 1 click (usually) to remove the tag. So seen purely as econ you are looking at a 3 cred swing in your favor. Above and beyond the cred/click changeover you do a meat damage. They probably aren't running with an empty hand, but 1 card might hit something good.
Prisec's tag, however, isn't really about economy. It is about click compression. The runner normally sees a run as a one-and-done kind of deal. Now the run isn't 'really' over until they have removed their tag. If they run last click they'll be ending the turn tagged. Still not so bad, but you can see where this goes.
Prisec is an upgrade, and not unique. There can be 2 prisecs in a server, or three. It can live in central servers, or remotes. It can live with Snare! or an advanceable upgrade. You can come out of a run with 2 or more tags, and a mauled hand. Even just running into an Argus Security: Protection Guaranteed agenda with a Prisec is a significant hit.
The brief tagged state is useful for Harishchandra Ent.: Where You're the Star , letting them see the runner's hand. SYNC: Everything, Everywhere makes the tag either more difficult to get rid of or more useful for the corp.
Further, Prisec doesn't just give you a tag. It causes you to end a run tagged. Dedicated Response Team anyone? Run into a server with a Prisec and they rez a DRT in the Jackson window and you've just sucked up 3 meat damage and a tag.
And, heck, the paid response window after they hit the Prisec is as good of a time as any to rez a Zealous Judge . Yet more click compression! Now the runner has to remove the Prisec tag, then run the ZJ and trash him. Hope he wasn't behind a Data Raven.
If you are playing a deck that goes for flatline and doesn't try to keep the runner out then slot 3 of these. You won't regret it.