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Matt Decker uses his rank to take control of the Enterprise, whereas Will Decker is temporarily removed from command of the Enterprise by Kirk.
Matt Decker’s poor call resulted in the deaths of his entire crew and the crippling of his ship, but Will Decker directly saves the Enterprise by belaying Kirk’s order regarding phaser fire which would’ve been a fatal mistake stemming from Kirk’s lack of familiarity with the recently finished refit.
The Doomsday Machine is one of only a handful of entities ever seen that is explicitly stated to have originated from outside the Milky Way galaxy, but V’Ger ultimately turned out to be a highly evolved probe from Earth itself.
Matt Decker dies in a failed attempt to destroy the Doomsday Machine (although his idea does give Kirk the inspiration he needs to actually destroy it), but Will Decker willingly chooses to merge with V’Ger. Secondarily to this, Matt‘s story ends with him unambiguously killed off, but Kirk decides that listing Decker as KIA would be inaccurate and declares him and Ilia “missing” instead.