Both are used in conversation to show negation, meaning “not good at all”. These negative answers may imply a polite and modest flavor when the speaker is being flattered, but a scornful flavor when someone else is praised. For example, “那本小说大家都说好，你觉得怎么样？” “好什么好， 乏味透了。”(Everyone says that novel is good, what do you think about it ?- Good ? No ! It is rather borning.)
Used when the speaker considers something is not true or not sensible. It is a negative comment with a discontented or scornful flavor. For example, “什么呀，这条广告纯粹是骗人的，这种药一点儿功效也没有。” (It’s so disappointing! This advertisement is entirely false. This medicine is not effective at all.)
Used when the speaker consider that the other side has a wrong idea about the relationship between two things or has made assertions without good grounds. For example, “你这是哪儿跟哪儿呀，小兰是王平的妹妹，怎么可能是他的女朋友呢？” (It is ridiculous! Xiao Lan is Wang Ping’s younger sister. How could she be his girlfriend ?”).
Both are used to express disagreement. “得了吧” has quite a strong tone of contempt and retort. “算了吧”may have a dissuasive flavor beside the negative one. For example, “就他那唱歌水平，还想到专业歌手？得了吧！” “算了吧，你们都说错了。”.
Used to express negative when others say something absurd. For example, “听说你要结婚了，恭喜，恭喜！” “笑话！我连女朋友都还没有呢，结什么婚！” (I was told that you are going to married. Congratulations!-That’s ridiculous! I don’t even have a girlfriend!).
Used to express approval of the other side in a conversation. It means “Yes, it’s true.” Or “I think so.” For example, “天气越来越热了。” “可不是嘛，毛衣都穿不住了。”(It is getting warmer and warmer,- You are right. It is too warm to wear a sweater.)
Used to express completely approval of the opinion of the other side in a conversation in a straightforward tone. For example, “你看看现在的糖果，包装越来越漂亮，里边的东西却越来越少。” “没错儿，上星期我买了一盒人参糖，里面有三层包装。” ( look at the candies now. The packaging becomes prettier and prettier, but the contents become less and less.- Absolutely right. I bought a box of ginseng candies last week. There were three layers of packaging inside the box! )
The speaker may not agree with certain opinion at the very beginning, but he/she approves of it after taking it into consideration. For example, Xiao Wang’s family planned to go shopping and go to the park on Sunday. Xiao Li, Xiao Wang’s wife, wanted to go shopping first. Xiao Wang said, “如果先买了一大堆东西，怎么逛公园呢?” Xiao Li said, “可也是，那就先去公园吧。”
Used to praise someone or something in a very strong tone. For example, “小张才学了半年汉语，HSK 就拿了个中B ，真是不简单！”