If I am angry at the person who is wanting to talk about it, I frequently will want to think about it for quite awhile before I talk about it. The reason for this is that I like to try to formulate a way of approaching the problem that will be least offensive. The pro is that by taking some time to think, I often calm down and can get to the bottom of what is really bothering me. The con is that often I will sit and think about it for so long that I decide to not address the problem at all, which means that NEXT time it's a problem, my emotional response to that problem is magnified.
If I am angry at someone else, I will usually want to talk about it with someone. However, I am not a gossip and won't want to just vent to anyone who can hear me. I'll find someone close to me (family member or best friend) and I will bitch about it. If that person acts uninterested or like they wish I would stop talking, it aggravates me to no end. Usually I am looking for validation that my feelings are not ridiculous and that I have a right to be upset. However, I usually prefer to vent to someone who will also approach me practically and honestly. Usually it's good to hear "I'm sorry" (to me, translated is "it's ok that you feel this way") "but maybe that's not what so-and-so meant" (translated "it will help if you try to look at this situation objectively") or "Why don't you try _____?" (translated "I want to help you mend this situation if possible" or "You have the strength and ability to mend this."). I hope that makes sense.