One of the biggest differences would be found in the textual basis for the OT. The RSV, being older, doesn’t take into account recent archaeological finds like the Dead Sea Scrolls. The NRSV does.
Also, you will notice that the book of Tobit in the RSV is shorter than in the NRSV, or NABRE for that matter. Here is a helpful explanation from the NABRE intro to Tobit:
Written most likely in Aramaic, the original of the book was lost for centuries. Fragments of four Aramaic texts and of one Hebrew text were discovered in Qumran Cave 4 in 1952 and have only recently been published. These Semitic forms of the book are in substantial agreement with the long Greek recension of Tobit found in Codex Sinaiticus, which had been recovered from St. Catherine’s Monastery (Mount Sinai) only in 1844, and in mss. 319 and 910. Two other Greek forms of Tobit have long been known: the short recension, found mainly in the mss. Alexandrinus, Vaticanus, Venetus, and numerous cursive mss.; and an intermediate Greek recension, found in mss. 44, 106, 107. The Book of Tobit has also been known from two Latin versions: the long recension in the Vetus Latina, which is closely related to the long Greek recension and sometimes is even closer to the Aramaic and Hebrew texts than the Greek is; and the short recension in the Vulgate, related to the short Greek recension. The present English translation has been based mainly on Sinaiticus, which is the most complete form of the long Greek recension, despite two lacunae (4:7–19b and 13:6i–10b) and some missing phrases, which make succeeding verses difficult to understand and make it necessary to supplement Sinaiticus from the Vetus Latina or from the short Greek recension.
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