In the Amidot of the Yamim Nora'im, in the blessing Kdushat Hashem, in Nusah Sfard four paragraphs beginning ובכן are added. In Nusah Ashkenaz, three are added.
In Avinu Malkeinu on Rosh HaShanah, in Nusah Sfard the custom is to omit the petitions that mention sin (I don't know if this is true for all editions of Nusah Sfard). In Nusah Ashkenaz the petitions are recited.
In the silent Amidah of Rosh HaShanah Musaf, in Nusah Sfard the shofar is sounded after each of the three middle blessings, and the paragraph HaYom Harat Olam is recited by each individual at each of those points (though in the nusah of the B'al Ha-Tanya, the paragraph is not recited). In Nusah Ashkenaz there is no sounding of the shofar in the silent Amidah.
I don't think differences in the selection of the piyyutim for Rosh HaShanah break down by Nusah Sfard/Ashkenaz distinction. (But for Yom Kippur, there is a distinction in the selection of the piyyut used for the Avodah in Musaf).