Since you're asking whether Giant Slayer or Last Whisper is better, that means you can't have 2300 g or more, since then you'd be able to buy both. So, there are 3 cases here:

• You have 1875g+, enough to buy Giant Slayer + Pickaxe (which builds into Last Whisper)
  
• You have 1650g+, enough to buy Last Whisper + Long Sword (which builds into Giant Slayer)
  
• You have 1300g+, enough to buy Last Whisper or Giant Slayer without anything else
  

I assume you're gonna be buying only the items that build into Lord Dominik's Regards, so you're not interested in buying other items, I also assume you have at least 2 item slots available, for all the cases.

Case 1:

Option A: Giant Slayer + Pickaxe
* +35 ad
* +10% bonus physical damage against enemy champions who have 500 or more more maximum hp more than you do

Option B: Last Whisper + Long Sword
* +35 ad
* +30% bonus armor penetration

In this case, the difference is only in the passives, which makes the comparison much easier. Since bonus armor means any armor you have other than your base armor, which (the base armor) includes armor per level, that means the bonus armor of any given champion is his total armor minus his base armor. If anyone on your team has Black Cleaver or an ability that reduces (not penetrates) the enemies' armor, then multiply the enemies' total and bonus armor by 1 - X, where X is the % of armor reduction divided by 100. Flat armor penetration doesn't change the calculations, unless you have enough that the target would get below 0 armor (which can't happen with flat armor penetration, thus some of it will be wasted, thus reducing the effectiveness of Last Whisper), then it does, but for this case we'll assume that you don't. Other percentage armor penetration sources will change them too, since they stack multiplicatively with each other, however, other than Darius' E, Yasuo's R and GP's E there are no other percentage armor penetration sources in the game, so we'll assume you're not playing Darius, Yasuo or Gangplank. So, 10% bonus physical damage equals 10% bonus physical damage. 30% bonus armor pen equals how much % bonus physical damage? This is calculated by comparing the physical damage reduction before the armor pen, and after. For example, 100 base armor + 100 bonus armor = 200 armor. 200/300 = 0.67 That equals 33% physical damage inflicted. With 30% bonus armor penetration, the armor becomes 100 base armor + 70 bonus armor = 170 armor. 170/270 = 0.6296 That equals 37% physical damage inflicted. 37/33 = 1.121, so that's a 12.1% increase in physical damage. So, against a target with 100 base armor and 100 bonus armor, Last Whisper provides more physical damage than Giant Slayer. However, what about the other cases, with differents amounts of base and/or bonus armor? Well, I did the math with a quick program I wrote, so here's the table, where the answer signifies whether Last Whisper provides more damage vs those amounts of base and bonus armor than Giant Slayer, or not. I've included common amounts of base and bonus armor, if the amount is not present, simply pick the closest one to it: