The impact on an Eirene RR4 is [i]slightly[/i] higher than the Thousand Yard and LDR 5001, so your damage [i]may[/i] be different depending on the sniper you choose. (slightly = 3 impact points). I don't think the numbers change in the video, but yeah.
And if your Eirene RR4 has Luck In The Chamber, don't use it as that would mess up your damage numbers. If you still have a Eirene package for the Gunsmith, he's currently selling a Void Triple Tap Eirene, so you can do exactly what he did in the video.
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The impact difference is actually a visual bug and database bug. It shows as slightly higher in game and 34 impact vs 31 impact on the database, however when you use it the damage is exactly the same. For example, the LDR and Eirene both did 58315 damage with both Weapons and Illuminated here. ^^ The luck in the chamber is a good point though!