Vader's men has a history unlike most others. As Kaminoan clones, they are superior to Spaarti clones and ordinary human recruits. As veterans of the Clone Wars, they are battle-hardened against droid and organic enemies alike. As the legendary 501st Legion, they are the ones who executed Order 66 at the very heart of the Jedi Order itself: the Jedi Temple. They are one of the most loyal and most elite force in the Galactic Empire, trusted by the Emperor himself.
Grand Admiral Thrawn's army may not enjoy the same prestigious history but they are a class above the rest nonetheless. His style of generalship emphasises on creative independent thinking (not unlike the advantage Kaminoan clones enjoyed), a willingness to question authority, and a personal conviction to serving the Empire. Unlike ordinary Imperials with blind obedience drilled into them, Thrawn's men are much more effective soldiers and, together with the brilliance of Thrawn's genius, it's truly formidable indeed against otherwise-insurmountable odds. The Emperor regularly entrusts upon Thrawn to deal with crisis in the Empire as well as longer term strategic interests in the Unknown Regions while the bulk of the Empire's attention is upon the Rebellion.
How does the two armies compare against each other, if we look solely at their historical battle records? How did they perform when going through similar combat situations?