Objection 1. It would seem that anger is more grievous than hatred. For it is written (Proverbs 27:4) that "anger hath no mercy, nor fury when it breaketh forth." But hatred sometimes has mercy. Therefore anger is more grievous than hatred.
Objection 2. Further, it is worse to suffer evil and to grieve for it, than merely to suffer it. But when a man hates, he is contented if the object of his hatred suffer evil: whereas the angry man is not satisfied unless the object of his anger know it and be aggrieved thereby, as the Philosopher says (Rhet. ii, 4). Therefore, anger is more grievous than hatred.
Objection 3. Further, a thing seems to be so much the more firm according as more things concur to set it up: thus a habit is all the more settled through being caused by several acts. But anger is caused by the concurrence of several passions, as stated above (Article 1): whereas hatred is not. Therefore anger is more settled and more grievous than hatred.
On the contrary, Augustine, in his Rule, compares hatred to "a beam," but anger to "a mote."
I answer that, The species and nature of a passion are taken from its object. Now the object of anger is the same in substance as the object of hatred; since, just as the hater wishes evil to him whom he hates, so does the angry man wish evil to him with whom he is angry. But there is a difference of aspect: for the hater wishes evil to his enemy, as evil, whereas the angry man wishes evil to him with whom he is angry, not as evil but in so far as it has an aspect of good, that is, in so far as he reckons it as just, since it is a means of vengeance. Wherefore also it has been said above (Article 2) that hatred implies application of evil to evil, whereas anger denotes application of good to evil. Now it is evident that to seek evil under the aspect of justice, is a lesser evil, than simply to seek evil to someone. Because to wish evil to someone under the aspect of justice, may be according to the virtue of justice, if it be in conformity with the order of reason; and anger fails only in this, that it does not obey the precept of reason in taking vengeance. Consequently it is evident that hatred is far worse and graver than anger.
Reply to Objection 1. In anger and hatred two points may be considered: namely, the thing desired, and the intensity of the desire. As to the thing desired, anger has more mercy than hatred has. For since hatred desires another's evil for evil's sake, it is satisfied with no particular measure of evil: because those things that are desired for their own sake, are desired without measure, as the Philosopher states (Polit. i, 3), instancing a miser with regard to riches. Hence it is written (Sirach 12:16): "An enemy... if he find an opportunity, will not be satisfied with blood." Anger, on the other hand, seeks evil only under the aspect of a just means of vengeance. Consequently when the evil inflicted goes beyond the measure of justice according to the estimate of the angry man, then he has mercy. Wherefore the Philosopher says (Rhet. ii, 4) that "the angry man is appeased if many evils befall, whereas the hater is never appeased."
As to the intensity of the desire, anger excludes mercy more than hatred does; because the movement of anger is more impetuous, through the heating of the bile. Hence the passage quoted continues: "Who can bear the violence of one provoked?"
Reply to Objection 2. As stated above, an angry man wishes evil to someone, in so far as this evil is a means of just vengeance. Now vengeance is wrought by the infliction of a punishment: and the nature of punishment consists in being contrary to the will, painful, and inflicted for some fault. Consequently an angry man desires this, that the person whom he is hurting, may feel it and be in pain, and know that this has befallen him on account of the harm he has done the other. The hater, on the other hand, cares not for all this, since he desires another's evil as such. It is not true, however, that an evil is worse through giving pain: because "injustice and imprudence, although evil," yet, being voluntary, "do not grieve those in whom they are," as the Philosopher observes (Rhet. ii, 4).
Reply to Objection 3. That which proceeds from several causes, is more settled when these causes are of one kind: but it may be that one cause prevails over many others. Now hatred ensues from a more lasting cause than anger does. Because anger arises from an emotion of the soul due to the wrong inflicted; whereas hatred ensues from a disposition in a man, by reason of which he considers that which he hates to be contrary and hurtful to him. Consequently, as passion is more transitory than disposition or habit, so anger is less lasting than hatred; although hatred itself is a passion ensuing from this disposition. Hence the Philosopher says (Rhet. ii, 4) that "hatred is more incurable than anger."
Source: Summa Theologica (New Advent)