Interesting question! James seems to find lots of qualities to admire in Emerson.
For example, he believes that Emerson is one of the few "whose singularity gives a note so clear as to be victorious over the inevitable pity of [death]." Maybe we can extrapolate from this that James values the ability to have a lasting impact that will do good to not only one's present time, but also to the people of the future, such that
the soul's note, the spiritual voice, rises strong and clear above the uproar of the times, and seems securely destined to exert an ennobling influence over future generations.
James also seems to value knowledge of oneself and the ability to stay true to not only one's character, but also one's limitations:
What gave a flavor so matchless to Emerson's individuality was, even more than his rich mental gifts, their singularly harmonious combination. Rarely has a man so accurately known the limits of his genius or so unfailingly kept with them.
He praises "loyalty to [one's] personal type and mission." Emerson apparently worked hard to preserve his autonomy, refusing to be "entrapped into services" or enlisted by "causes" other than the one he had set forth for himself. To me it's not clear how James feels about this; though he works hard to make it a virtue ("but we, who can see things in moral liberal perspective, must unqualifiably approve the results"), he also mentions that Emerson refused to take part even in campaigns he believed in, like the fight against slavery. He believed those tasks were "duties for other men and not for him," as he had his own ideals to defend and advance. (And so perhaps we come to understand what James means when he speaks of fidelity to the "limits of his genius.")
In any case, it seems James admired Emerson's freedom and his enduring ability to stick to his convictions: "The only way to be true to our Maker is to be loyal to ourselves," he says while praising Emerson's "non-conformist" spirit and determination to do precisely what he wanted (and perhaps only what he wanted), not "consent[ing] to borrowed traditions and living at second hand." Emerson was "true to [his] own private conscience."
He also values those whose look with eyes unclouded by the judgments of others, and who seek out the truth no matter what other people tell them: "In seeing freshly, and not in hearing of what others saw, shall a man find what truth is."
It seems James deeply respects Emerson's determination to be true to himself as he supports the "indefeasible right to be exactly what one is, provided one only be authentic."
And finally, it seems James likes Emerson's discriminating taste; the poet did not "hurrah for the Universe" like Walt Whitman, but rather cheered for the world on the condition that it populate itself with "worthy specimens."