Both emotions are destructive, and it would be hard to say if one is more harmful than the other. And they usually go hand-in-hand; hatred almost always leads to anger, and anger almost always leads to hatred.
The real problem, however, is that both anger and hatred are seldom just inner feelings or emotions that we keep bottled up inside us. Instead, they almost always spill over into actions -- and those actions are always destructive, both to us and to others. Even if we don't lash out and hurt someone physically, our words of anger and hatred can destroy our relationship. The Bible rightly says, "Hatred stirs up conflict" (Proverbs 10:12).
Does God ever get angry, or does He ever hate? It may surprise you, but the answer is "yes." But God's answer is far different from ours, because it comes from His hatred of sin. God loves us and knows the terrible things sin does to us -- and that makes Him angry. Perhaps you've heard the old saying, "God hates the sin, but He loves the sinner."
The real question, however, is this: Have we allowed the sin of hatred or anger to take root in our souls? The only lasting cure is to allow Christ to rule us, and let His love fill our hearts and minds every day. Make sure of your commitment to Christ, then ask Him to give you a new love for others -- even your enemies. The Bible says, "Be like-minded, be sympathetic, love one another, be compassionate and humble" (1 Peter 3:8).