It depends entirely on your ship's purpose and design constraints.
Once a PC ship gets to a higher tier and the ship's budget is large enough, the direct cost of a weapon becomes less important than the actual performance of the weapon, and the persistent particle beam is the strongest generic damage gun most PCs will have access to. It's beaten out by a few things, but they all have some pretty significant strings attached. So at some point the PPB becomes a serious consideration just because it has so much power in a single action. It'll even beat out missiles once you can afford to link a pair.
When that happens depends on a lot of different things. If you're working with ship budget rules, it'll happen later than it would otherwise. If you're in a less combat-oriented campaign, it might not happen at all if you can find other things to spend the BP on. If you're playing the existing APs, you might not feel much pressure to upgrade because a bit of optimization goes a long way right now.
It's not worth it at low levels. It can very easily be worth it at higher levels if you don't opt for some of the more interesting options.
For non-PC ships, it depends on all of that in just the same way, with an extra consideration of how much you want to hurt your players.