PD might give better AS and crit chance, along with ignoring unit collision, but just about everyone I see prefers Statikk Shiv over it because of the chain lightning proc and because it builds out of Avarice Blade.
It honestly feels like the two are competing for the same niche, but Statikk Shiv is just better.
Onegarion2 votesI tend to get Statik only when my champion either greatly benefits, I'm behind, or we have no wave clear. The wave clear really isn't that much of a benefit since the passive static isn't that great when it comes to damage or overall wave clear. If I'm behind it lets me farm a little safer and catch up a bit more albeit very little. Some champions just work better mainly the mobile ones that can get more procs in. Overall though if I'm ahead or need to duel more I go PD.
Kuroi861 votesPD is better for dueling, it grants better stats and it's passive means you can't be body blocked. If you've already got good wave clear and are looking for something to give you better dueling and single target power, the Phantom Dancer is your pick.
Statikk Shiv is good for pushing and team fights. It may not give as much in stats, but the Statikk proc can really help you push those minion waves and can even give you some AOE to work with in team fights, possibly extending your range by a little bit via the Statikk.
Worgslarg1 votesI get shiv if my team needs waveclear, or the proc is more useful than normal on the champion.(Eg Yi, Yas because their dashes count for the recharge, and its really good on them otherwise.
Sozan51 votesStatikk is better if your AD is low, while PD is better when your AD is higher - as far as DPS goes.
In my example with 55% bonus AS (25% from boots, 5% from masteries and 25% from level (which can be anywhere between level 7 and impossible - depending on ADC), Statikk procs once every 4 seconds (which might be hard or even impossible, as with that Attack Speed it takes about 8 seconds to stack it with autoattacks alone - and while movement stacks it fast you can actually lose on DPS by moving too much).
With IE the border is at 130 AD. Below it SS will deal more DPS than PD. Above it - PD will deal more DPS.
Without IE the border is at 140 AD.
At 200 AD with IE the difference is about 23 damage per second in favor of PD and that is obviously including the Statikk Passive. That's actually a pretty big difference, especially considering that you won't always get statikk every 4 seconds.
Another thing to keep in mind though - LW or any other kind of armor penetration doesn't apply to Statikk Shiv (as it's magic damage), but the opposite is true as well - armor doesn't work on Statikk (so it might be worth it if your enemies completely neglected MR - while it will be utterly useless if they have a lot of it - 106 MR is enough to cut your damage in half from Statikk if you took the Penetration mastery (if you didn't it's obviously 100) - and unlike physical damage you won't be getting more penetration (unless you are Kog or Varus, then you actually can build a bit hybrid with Void Staff if enemies stack armor all day - still, might be not the best choice).
Also, SS will nearly always result in higher burst damage, so keep that in mind.
Anyway, I think that PD will be a better choice in most scenarios, though you can get a lot of Statikk if you will rush it (which kinda defeats the purpose of Avarice Blade). Also it costs a bit less, making it easier to build if you have to.
Don't bother building it for wave clear, it's really not good for this. If you really need wave clear you are better off with Runaan (which isn't THAT bad of an item, considering that it can potentially double your DPS, but on multiple targets. Also, as a side note - Lucian passive does interact with Runaan and shoots the bolts twice (and their damage is not lowered)).
