The poems are similar in that both speakers are trying to come to terms with aging and death. However, the speakers differ very much in how they react to old age and dying.

Roethke's speaker is at peace with aging, and describes it in positive terms. He says of growing older:

The lost self changes,
Turning toward the sea,
A sea-shape turning around,—
An old man with his feet before the fire,
In robes of green, in garments of adieu.

An old man before the fire in green robes is a pleasant image that depicts one's waning years as a warm and comfortable time.

In contrast, Yeats's narrator dislikes aging, seeing an old man, in general, unless his soul "sings," as

. . . but a paltry thing,

A tattered coat upon a stick