The Greek genocide was not as large as the Armenian genocide, and did not have the same geopolitical consequences as the latter. Also, it tends to just fall into the extremely long history of hostile Greco-Turkish relations, and so as an individual event it isn't as important.

Only 450,000-700,000 Greeks perished during this persecution, compared to about 1,500,000 Armenians. Considering it is estimated that this was 3/4 of Armenians in the Ottoman empire, their persecution was much more devastating. In the aftermath, we have an extremely tiny and weak Armenian state that is forced to be incorporated into the USSR who are eager to take advantage of a potential conflict with Turkey as they covet access to the Mediterranean and the greater oceans through the straits of Turkey. This results in the coalition of the west backing Turkey wanting to curb the influence and power of the USSR.

TL;DR

Greeks and Turks have been at each others throats for thousands of years, Turkish persecution of Armenians started at the dawn of the 20th century and really their only goal was to wipe them out. Greater geopolitical consequences between the USSR and the West.

Here's a previous discussion on the topic.