Rashi (Sukkah 46) indicates that the bracha of she'asa nissim is recited on the neiros only after the bracha of she'hechiyanu (this is also the view of the Mes Sofrim). Why should hadlakas menorah be different in this regard from kri'as hamegillah, where the bracha of she'asa nisim precedes she'hechiyanu?
The Rogatchover explains that there are two seperate miracles which Chanukah celebrates: 1) the victory over the Hellenists; 2) the miracle of the oil/menorah. These different miracles give rise to two distinct kiyumim of pirsumei nisa, one connected directly with the act of hadlakas menorah, one connected more generally with the celebration of the day.
The bracha of she'asa nisim recited on Purim is directly connected only with the mitzvah of kri'as hamegillah; it therefore comes immediately after the bracha on kri'ah. The bracha of she'asa nisim recited on Chanukah, however, is not only directly related to the mitzvah of pirsumei nisa through hadlakah; it also commemorates the military victory. Therefore, it is placed only after the she'hechiyanu, after the act of hadlakah is complete.
This also explains why one may recite the bracha of she'asa nisim upon seeing a menorah (according to some Rishonim only if one will not light later; according to other Rishonim even if one will light). Tosfos (Sukkah 46a) wonders why we do not find such a bracha by any other mitzvah -- there is no bracha on seeing a sukkah, on seeing a piece of matzah, etc. The difference between Chanukah and other mitzvos is that the bracha of she'asa nisim is not connected only with the mitzvah act of hadlakah, but rather also serves as a seperate blessing of thanksgiving. (See Reshimos Shiurim on Sukkah citing R' Soloveitchik for a different approach.)
These two themes are hinted at in the Rambam's double-language, "l'har'os u'legalos hanes." In addition to demonstrating (l'haros) to all the obvious miracle of the menorah, our mission is to reveal (l'galos) the hidden miracle of the military victory over the Greeks.
The Rogatchover adds a fascinating chiddush l'halacha. Since batlah megillas ta'anis, that element of pirsumei nisa connected with the military victory is no longer celebrated. For this reason we are not required to light menorah in public and we no longer are required to recite she'asa nisim upon seeing a menorah. Our kiyum of pirsumei nisa is limited in its fulfillment simply to the act of lighting in private. (A novel explanation as to why the minhag is not to light outdoors even in our times when no tangible sakanah exists!)