1) In the time of the Ge'onim there was a minhog to say a perek of Tehillim before ma'ariv. The Ari z"l re-instituted the minhog to say a perek (Shir Hamaalos).
2) Shir Hamaalos came into minhag Ashkenaz since it was first said by a small group, Chevras Maariv Bizmano (those who davened Maariv after Mincho anyway had no need for this, as explained above). Later when many people began davening Maariv Bizmano, they davened like the initial group, and that is how it became more common.
Mizmor Shir Chanukas Habayis, was not accepted in Ashkenaz, (besides the fact that the the historical dynamics mentioned above did not apply to it), because halachically there is a problem with saying it according to Minhag Ashkenaz, which holds that pesukei zimroh are said only
after Boruch She'omar, since all Brochos are done "Over La'asiyoson" - before the Mitzvoh that the Brocho is applying too.
FRBSH
As a side point - the Ari z"l never instituted Mizmor Shir as a separate mizmor before Boruch Sheomar, but rather as a mizmor to be said after Hodu, which by the Sepharadic minhog is before Boruch She'omar. Some say that according to Minhag Ashkenaz Mizmor Lesoudoh, which is said after Hodu, comes in place of Mizmor Shir according to the Sepharadim.
Michael