Let's take a look at that.
Throughout the course of the war, about two million men fought for the Union. Of those, 180,000 (approximately) were black, or less than ten percent of the total. The number of Confederate soldiers is uncertain, but is almost certainly less than a million men throughout the course of the war.
Most of the black soldiers were not employed in combat functions, partly because of racism on the part of white Union officers, partly because the Confederates tended to kill blacks who surrendered. There were of course notable exceptions like the 54th Massachusetts Volunteer Infantry.
The Emancipation Proclamation actually caused a net reduction in volunteers for the U.S. Army. The Irish immigrants in particular, who had volunteered in large numbers before, viewed blacks as a threat to their jobs, much the way working-class whites today often view Hispanic immigrants. So to the extent the Proclamation remedied a manpower shortage, it remedied a shortage that it had itself created.
Regarding the manpower differences between North and South, note that the Union had more than a 2-to-1 advantage in total population COUNTING the Southern slaves. (19 million compared to 9 million.)
You are presenting a false dilemma here. Those were not the only two motives, as Lincoln's own example testifies. It's clear that he did not believe in racial equality, but equally clear that he opposed slavery as a moral matter, because it was wrong to enslave even "racial inferiors." Among those who opposed the institution, that was probably the prevailing sentiment (although we may safely assume that black emancipationists didn't share it, I believe).
