The gemara (Archin 10) discusses why we say full hallel on some days and not others. Why no full hallel on Shabbos? Because, answers the gemara, Shabbos is not called a mo'ed, and we only say full hallel on a mo'ed. Why no full hallel on Rosh Chodesh, which is called a moed? Because, answers the gemara, there is no prohibition of doing work on Rosh Chodesh, which indicates that it is a different sort of mo'ed than the yamim tovim.
So why did we not recite full hallel yesterday? On Shabbos Rosh Chodesh all the necessary factors overlap -- it is Shabbos, so there is an issur melacha, and the day is called a mo'ed because it is Rosh Chodesh as well.
As we discussed once before (here), when two different kedushos hayom (or other logical halachic structures) overlap, one needs to investigate whether the two different factors co-exist side by side independently (what the Rogachover calles a harkava shichnit) or whether the two factors combine together to create a new synthesis (what he calls a harkava mizgit). In our case, if there was a new type of kedushas hayom created called Shabbos-Rosh Chodesh which was a synthesis of elements of both Shabbos and Rosh Chodesh, then perhaps one could argue the case for full hallel. But apparently that's not the case. The kedushas hayom of Shabbos and the kedushas hayom of Rosh Chodesh happen to coincide on the same day, but each retains its independence, each retains its shortcomings as a mechayeiv of hallel, and therefore, only partial hallel is recited.