Nietzsche's conception of the contrast of the Slave-Master morality contrast stands as just that, a contrast between two different but not necessarily fundamentally incompatible forms of morality. The contrast between the two is not that they value different and opposing ideals, but rather that master morality is an active morality, while slave morality is a reactive morality (here, especially section 10 of the Genealogy). The slave says "no" to life, to suggest that the instinct is something controllable and, hence, to apply morality to all one's ability to control one's urges, to circumvent the activity of one's power. Slave morality borrowed the distinction of "good" and "bad" and created "good" and "evil" as opposites. Thus, Nietzsche would class Hegel's Master-Slave morality as a sort of slave morality (this, even ignoring Hegel's claim that the slave class becomes stronger and triumphs) because it contrasts the Master and Slave morals as mirroring one another. Taken in Hegel's sense, Master morality and Slave morality stand in contradiction and require some kind of resolution if one is not to overtake and dominate the other, hence, the dialectical process. For Hegel, the historical circumstance of the domination of Master morality is no more than the domination of one side of the dialectical contrast which inevitably shall be eventually cease when the Master grows too weak and is overthrown by the Slave. This should also be contrasted with Nietzsche conception of the reason for the overthrowing of the Master: rather than being too weak, the Master remains strong and is only curbed from expressing their power, through the subversive strength of Slave morality, which demands that they say "no" to themselves.
It is this requirement of opposing position that likely creates Nietzsche's animosity to the dialectic; for Nietzsche, we are not speaking of good or bad in morality except as it relates to other aspects of existence (survival, improvement, culture, etc.). As he states again and again, the very question of morality is to be considered, and here he considers the primary method by which the world is classed within morality and contrasts it with other historical examples. Whereas Hegel takes the Master-Slave connection to be one which leads to some sort of historically inevitable conclusion, Nietzsche would not support any such conception (let alone Hegel's apparent belief in a form of socialism establishing the conclusion of the Master-Slave conflict).