Both of these poems focus on the plight of animals forced into an unnatural situation through capture by humans. Both of them eschew rhyme, which creates a more naturalistic, conversational tone: the speaker in each poem is contemplating the situation of the animal s/he is describing to the reader. Bishop's poem is significantly longer than Rilke's, but thematically they are very similar.
In Rilke's poem, the panther who is its subject is "weary." He has been behind bars for so long that there is seemingly "no world" behind them; he has lost his desire even to lift the "curtain" of his eyelids. His "mighty will" has been crushed by what has been done to him; he is now unable, or unwilling, even to fight. It is situationally implied, although not stated explicitly, that the panther is older in years.
The fish who is the subject of Bishop's poem, like Rilke's panther, has been captured and is now unwilling to fight his capture. Again, like Rilke, Bishop does not see this as evidence of weakness: just as the panther is "mighty," the fish appears "venerable" in its dignified lack of resistance, marks of its age visible on its scales. It is clear here, too, that there was once a greater force of will in this fish which has been beaten down by repeated human contact—in Rilke's poem, we see this in the glimmer of agency which appears, and then is gone, at the end; in Bishop's, we see it in the physical evidence of the fishhooks in his mouth, like "medals" won in former battles in which he was victorious.
For both fish and panther, however, the will to battle is over. Both are portrayed using the humanizing pronoun "he," and both are shown as mighty creatures who have been worn down over time. Bishop, unlike the speaker in Rilke's poem, has more active agency over the fish than Rilke's speaker does over the panther. At the end, moved by the fish's force of spirit, the speaker lets him go.