.44 Mag is a cartridge and Desert Eagle is a pistol. Therefore they cannot be compared.
The Desert Eagle comes in various calibers including .44 Magnum. The .50 AE is the bigger cartridge often used in the Desert Eagle, and almost always in movies. I will go out on a limb and assume that you mean this.
The .50 AE is a bigger and more powerful cartridge than the .44 Magnum.
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