In the musafs for Shabbat-Rosh Chodesh and the Yomim Tovim we bemoan our inability to offer the sacrifices because of the destruction of the temple. (That we do so only on the Rosh Chodesh which falls on Shabbat and not the "regular" Rosh Chodesh is dealt with here)
However, there is a subtle change in wording. On Yom Tov, we read that the Beit Hamikdash was destroyed " מִפְּנֵי הַיָּד שֶׁנִּשְׁתַּלְּחָה בְּמִקְדָּשֶׁךָ". However, on Shabbat-Rosh Chodesh we say (according to my Siddur Tefillah Hashalem) " מִפְּנֵי הַיָּד השלוחה בְּמִקְדָּשֶׁךָ"
[note -- the sefaria.org site and my artscroll have nishtalcha in both cases]
What would the difference be in terms of meaning and intent of the composer if one were to choose one rather than the other? Do they mean the same thing precisely or refer to exactly the same event?