Also, shadow sneak is too underpowered, and should not be relied upon as his main attack, shadow claw should be there instead. The saddest thing I regularly see since gen 6 started is people bring Aegislash in early on, and trying to set up right away, leaving them easily countered, then trying to shadow sneak even though it does pitiful damage.
They're close enough. Basically the only thing you forfeit by running Shadow Sneak over Shadow Claw is a chance to OHKO walls instead of 2HKOing them, and in return you're getting a priority attack that will slaughter any non-wall after Stealth Rock damage.
Here's calculations for walls:
Scenario: +6 Adamant Aegislash (no boosting item) vs. Defensive Skarmoy
+6 252+ Atk (custom) Shadow Sneak vs. 224 HP / 252+ Def Skarmory: 181-214 (55.35 - 65.44%) -- guaranteed 2HKO
+6 252+ Atk (custom) Shadow Claw vs. 224 HP / 252+ Def Skarmory: 316-373 (96.63 - 114.06%) -- 81.25% chance to OHKO
Conclusion: Shadow Claw has a high potential to OHKO, but should that fail, it is no better than Shadow Sneak.
Scenario: +6 Adamant Aegislash (no boosting item) vs. Defensive Gliscor
+6 252+ Atk (custom) Shadow Sneak vs. 244 HP / 248+ Def Gliscor: 198-234 (56.25 - 66.47%) -- guaranteed 2HKO
+6 252+ Atk (custom) Shadow Claw vs. 244 HP / 248+ Def Gliscor: 345-406 (98.01 - 115.34%) -- 87.5% chance to OHKO
Conclusion: Should Shadow Claw fail to OHKO, it takes the same amount of time as Shadow Sneak, BUT I would advise Shadow Claw against Gliscor because it can kill you with Earthquake if it catches you in Sword form unlike Skarmory.
Here's calculations for random bulky threats:
Scenario: +6 Adamant Aegislash (no boosting item) vs. Offensive Heatran
+6 252+ Atk (custom) Shadow Sneak vs. 0 HP / 0 Def Heatran: 304-358 (94.11 - 110.83%) -- 62.5% chance to OHKO
+6 252+ Atk (custom) Shadow Claw vs. 0 HP / 0 Def Heatran: 531-625 (164.39 - 193.49%) -- guaranteed OHKO
Conclusion: If you're running Stealth Rocks or Spikes, always go for Shadow Sneak. Otherwise, go for Shadow Claw.
Scenario: +6 Adamant Aegislash (no boosting item) vs. Choice Scarf Garchomp
+6 252+ Atk (custom) Shadow Sneak vs. 4 HP / 0 Def Garchomp: 333-393 (93.01 - 109.77%) -- 56.25% chance to OHKO
+6 252+ Atk (custom) Shadow Claw vs. 4 HP / 0 Def Garchomp: 582-685 (162.56 - 191.34%) -- guaranteed OHKO
Conclusion: Again, if you're running Stealth Rocks or Spikes, go for Shadow Sneak. Otherwise, Shadow Claw. (Though this matchup will likely never happen as if your opponent's Garchomp is alive, you probably aren't going to be able to hit +6 yet and you should use Aegislash as a pivot until Garchomp is down.)
Scenario: +6 Adamant Aegislash (no boosting item) vs. Choice Scarf Kyurem-B
+6 252+ Atk (custom) Shadow Sneak vs. 0 HP / 4 Def Kyurem-B: 318-375 (81.32 - 95.9%) -- guaranteed 2HKO
+6 252+ Atk (custom) Shadow Claw vs. 0 HP / 4 Def Kyurem-B: 555-654 (141.94 - 167.26%) -- guaranteed OHKO
Conclusion: With Stealth Rocks, Shadow Sneak is better. Otherwise, Shadow Claw.