League of Legends (LoL) Question: Last Whisper or Youmuu's Ghostblade?

Personally, I like building Yoummu's first on ADCs who have abilities that amplify their auto attacks. So Vayne for example, the active helps get off more procs since you can attack faster. Last Whisper is more of a late game item since early on your opponents won't have much armour. For melee assassins it's almost the same thing, take Zed for instance. He is an assassin but aaing is still a big part of his kit due to his passive. It's also great for chasing people down. But since he is an assassin I build both on him for the great armour pen. That said, there really isn't a reason to rush either item unless your opponents start building armour extremely early on. And it all really comes down to personal preference :3

They may seem to have the same stats, but they are pretty different in functionality.

Last Whisper is more what you buy to deal with heavy armour. If the enemy is starting to stack armour, then you need a Last Whisper. Generally you'll get this as a third or fourth, possibly fifth item if they start late, but you pretty much need a Last Whisper at one point in the game.

Youmuu's is more for dueling power. A Brutalizer is a very good early purchase as the flat armour penetration is very good for the early stages (I wouldn't recommend rushing it on ADCs though), and it's very cheap as well. A Youmuu's allows a Vayne to get a huge power spike relatively early for a late game hypercarry, so it's good for those. Additionally, if you plan to duel more often then get a Youmuu's. Youmuu's also synergises well with carries that have major steroids, such as Vayne, Lucian and Twitch.

Personally, I feel like it's better to compare a Youmuu's with Statikk Shiv or Phantom Dancer rather than a Last Whisper. Its place in your build is more similar to those items.

Yoummu's shouldn't be looked at as an alternative to LW. Get Yoummu instead of your ASPD item (or along with it) on stuff like Lucian, Vayne, Twitch etc.

it depends whether or not you're facing a tanky or squishy team (or if they have a very pesky tank like a Mundo, Malphite, or Rammus). Personally, on assassin's like a kha zix, Rengar, or Zed i prefer to run Youmuu's (also some very bursty adc's like vayne or twitch). Otherwise, i would get a Last Whisper, but to be quite honest it's all too situational to say which is better, just make a wise decision on the matter when faced with it in game.

Depending on the opponents' states
If they're Tanky get LW (35% armor pen.)
If they're squishy get YGB (20 Armor pen. and Attack speed buff is enough to wreck their faces + 20% Movment Speed to chase'em down)

Good Luck

Depends on the ADC, Vayne could get a Youmuus or Youmuus and LW. Twitch, Draven, Graves, Lucian, Jinx, Varus (basically any ADC that builds Bloodthirster other than Corki), also build both. Youmuus is always a second item after either your Ruined King (Twitch and Vayne) or Infinity Edge (Anyone else).
For any melee carry other than Shaco or Tryndamere who prefer Statikk, Youmuu's is core, also as a second item.

I don't like building either one.

They're both not very good items in the long run, at least for me they aren't. But if you can properly execute the active of Youmuu's, it makes it worth the buy.

Last Whisper, as said earlier, is good against high armor tanks, like a Rammus.

Lucian on ulti together with youmuu