So, PD vs. Shiv, from what I've learned and heard from better ADC mains, depends on the ADC pretty heavily. Building one over the other isn't bad or anything, but each champion is naturally going to prefer one over the other.
So, the more reliant you are on auto attacks to deal damage, the better Phantom Dancer is. Shiv actually deals more damage in short trades and is burstier, but when you fight for longer PD starts to overtake Shiv in damage pretty quickly. Champions like Vayne, Caitlyn, Ashe, and Draven prefer PD because they deal damage in auto attacks fairy exclusively. Miss Fortune, Lucian, Quinn, and Graves both use abilities to deal a lot of damage and, more importantly, want to burst enemies more than fight for a longer period of time if they can help it.
There's also a couple of other things to consider. If your team has weak waveclear, or if you're being pushed in a lot, Shiv is really good. If you're late game, Shiv's damage has fallen off and Phantom Dancer is probably better by now. If you're behind, Shiv is easier to build and typically ends up costing a significant amount less if you build Avarice Blade quickly. If I had to say what I'd normally build on every ADC I'd go... (note that I could be wrong on some of them, I don't play every ADC so some of them are more or less guesses).
Statik Shiv: Graves, Lucian, Miss Fortune, Quinn, Sivir (to synergize with her waveclear more than anything), Varus.
Phantom Dancer: Ashe, Caitlyn, Draven, Jinx, Kog'Maw, Tristana, Twitch, Vayne.
Vayne, Kog'Maw, Draven, and maybe Twitch (I don't play as him) might consider Shiv to help with poor waveclear.
Just my two cents.