In "Before I got my eye put out –," the speaker has, at least partially, lost her ability to see; the poem expounds upon how overwhelmed and ecstatic she would be if she were told that she could suddenly see all the everyday wonders of nature again. While she never utters the words "I cannot see," we know that she has lost at least one eye, and that if she could see once more, "The news would strike [her] dead" (line 17). Thus, her reaction appears to be one of great grief, but also of having resigned herself to a new norm, such that it is "safer" (line 18) to remain as she is.
In "We grow accustomed to the Dark –," the first line itself tells us that the speaker of that poem also finds new comfort after losing sight, but it is not a sorrowful transition; rather, when all goes dark, her eye "Adjusts itself to Midnight" (line 19).
Thus, the two speakers are actually reacting to similar circumstances, in that they lose the ability to see, whether by having an eye put out permanently or by the momentary setting of the sun. However, the speaker of the first poem seems to experience a shrinking of her world such that, even while she longs for the sights that she knows are out there, she does not think she could handle regaining those sights. The speaker of the second poem, meanwhile, experiences a momentary confusion before learning how to see in this new environment and continuing on. Both speakers, in different ways, learn to accept their dark new realities.
If the speaker of the second poem literally lost her eyes, she might still be able to navigate through her darkness, as she acknowledges that perhaps "the Darkness alters" (line 17) and not her actual eyes—as we know to be scientifically, technically, the case. Her darkness may be of a different nature than ours, more accommodating. However, she knows it might also be "the sight" (line 18) that adapts to the Darkness, and thus we may never know whether literally losing her sight would affect her reaction to the night.