In her book Amy Beach, Passionate Victorian: The Life and Work of an American Composer, which was published twenty years ago, Adrienne Fried Block recognized that Beach's "Gaelic" Symphony was "both inimitably her own and at the same time influenced by the 'New World' Symphony's use of folk idioms."
The influence may have also involved key choice as summarized in the table below, which provides some information about the first movement of each symphony. The numbers indicate measures and are distributed proportionally in the figure, unless measure markers are too close, as in the case of Dvořák's mm. 396 and 400. The counting of Dvořák's measures begins after his twenty-three-measure slow introduction. The vertical/diagonal lines indicate the degree of discrepancy between the time -- proportional to each work's sonata-form span -- that the keys (along with their accompanying formal sections, in some instances) arrive in each movement.
However, in their recapitulations (Recap.), both first movements proceed through the keys of E minor, G-sharp minor, and A-flat major before returning to E major and then finally E minor. These choices of keys for a recapitulation's secondary themes (#iii and #III enharmonically) are extremely unusual for a nineteenth-century sonata-form work, which suggests that Beach's keys were modeled after Dvořák's. However, while Dvořák's keys and two secondary themes align (S1 in Gm and G#m, S2 in GM and AbM), Beach restores her S2 to E major, which is the traditional tonal adjustment of secondary themes in a sonata-form movement. Dvořák never provides a theme or even a cadence in E during the secondary-theme portion of his recapitulation, upending a time-honored convention. For this reason (and other reasons, which I may revisit in a later post), Beach's movement is more conservative, more "old world."
Beach took issue in the mid-1890s with Dvořák's recommendation that American composers should use "negro melodies" in cultivating a distinctively American music. In her biography, Block relates how Beach opposed this view, "believing that blacks were no more 'native American' than 'Italians, Swedes or Russians,'...rather, she believed that composers should look to their own heritage." Beach's incorporation of Gaelic folk songs in her symphony makes it clear that she is looking back over the pond for inspiration, but her use of more traditional European relationships among key, theme, and form than what occur in Dvořák's symphony suggests a more subtle way to achieve her posture, which is at once critical and tradition-oriented.