Chaim Brisker differentiated between yaaleh v'yavo and teil tal u'matar. R' Chaim assumed that yaaleh v'yavo is *not* part of the definition of the bracha of avodah, but rather is recited because there is a separate chiyuv of mentioning me'ein ha'meora, what makes the day special, be it rosh chodesh or yom tov. Nafka minah: according to this approach, if you forget yaaleh v'yavo at mincha today, you would not daven a tefilas tashlumin at night. You already fulfilled your chiyuv of tefilah at mincha time, and once rosh chodesh is over you can no longer mention me'ein ha'meora, so you gain nothing by davening maariv twice. Were yaaleh v'yavo part of the definition of the bracha of avodah, leaving it out would be like leaving out a bracha of shmoneh esrei and you would have to daven tashlumin at maariv.
In contrast to yaaleh v'yavo, R' Chaim assumed that tein tal u'mater is an intrinsic part of the bracha of bareich aleinu. Leaving it out is like missing part of a bracha in shmoneh esrei.
R' Tzvi Pesach Frank asked: The halacha is that if you miss saying tein tal u'matar, you can add it in the middle of the bracha of shema koleinu. If mentioning tal u'matar is a separate chiyuv hazkara, like mei'ein ha'meora, this makes perfect sense. You missed the hazkara in one spot, so you can add it in another spot. But if tein tal u'matar is part of the bracha of bareich aleinu, then if you are missing part of one bracha, how can you make it up by sticking the words in another?
See R' Eliyahu Bakshi Doron's discussion here.