I heard the following explanation from a Ba'al Toke'a:

1) Tosfos in Rosh Hashana (33b, 11 lines from the bottom of the page) cites Rav Amram Ga'on who says that at the end of the Teki'os, one Teru'ah is sounded. The Ba'al ha'Me'or (page 12a of the pages of the Rif, DH v'Ani Omer) cites Rav Sa'adyah Ga'on and Rav Amram Ga'on as saying that the reason for this Teru'ah is to confuse the Satan.

2) Tosfos (Rosh Hashana 16b, DH Kedai) explains the idea of confusing the Satan. The verse in Yeshayahu 27:13 tells us, "On that day the Shofar Gadol will be blown." When the Satan hears the Shofar the second time, he thinks that this must certainly be the great Shofar and that the time has come for the Satan to be swallowed up. He gets confused and is not able to be "Mekatreg" (make accusations) against Klal Yisrael.

3) The Shulchan Aruch (Orach Chayim 596) cites Rav Amram that at the end of the Tefilah, a Teru'ah Gedolah is blown. This is the Sefardic custom, but the Mishnah Berurah (#1) cites the Mateh Efrayim who says that it is not our custom; instead, we blow a Teki'ah Gedolah. However, one may say that even though we blow a Teki'ah Gedolah instead of a Teru'ah Gedolah, the idea behind this is still the same -- namely, to confuse the Satan.

4) According to the above explanation, we can say that since the effect of this final Teki'ah is to remind the Satan of the Shofar Gadol, therefore it is called "Teki'ah Gedolah," an not "Teki'ah Arukah."

G'mar Chasimah Tovah,

Dovid Bloom

Here is a simpler way of answering your question. The word "Gedolah" also includes being "Aruchah." A source for this is the verse which discusses the Kohen Gadol. The Torah (Vayikra 21:10) talks about "the Kohen who is greater (Gadol) than his brothers." The Yalkut Shimoni there (according to one version) states that one of the respects in which the Kohen Gadol must be greater than his brethren is "b'Midah" -- "in size." The Torah Temimah writes that this means that he must be taller than his collegaues. The Torah Temimah compares this to the Gemara in Shabbos 92a, where we learn that the Shechinah rests only on a "Ba'al Komah," a tall person.

We learn from there that the word "Gadol" also means physically tall. Accordingly, we may add that a "Teki'ah Gedolah" means, apart from the other deeper meanings, that the Teki'ah is longer than the other Teki'ot.

Dovid Bloom