遭遇 is usually come with bad things such as "tsunami, storm or disasters" OR "something stolen, or raped" It is unexpected. 经受 is expected somehow. He knew it is dangerous to be in Afghanistan, but he also knew to be a great journalist he has to 经受 the experience of real war.

经受(suffer from ) is passive voice, mostly negative it's a verb like 经受失明之苦 (suffer / blindness / sad ) suffer from blindness 遭遇is neutral (but mostly is negative) it's a noun or verb it could be suffering or experience check this out 1. 得知他痛苦的[遭遇]后，我忍不住同情他。 After learning of his [sufferings], I couldn't help sympathizing with him. 2. 一个人只要将自己的大脑与计算机连接起来，进入Cyberspace，就可以体验在该空间的一切[遭遇]。 Once his brain was linked with the computer, a man would undergo all [experiences] in　the space. 3. 我希望我永远不会再[遭遇]到这种不愉快的经历。 I hope that I shall never again have to [undergo] such unpleasant experience. 4. 遭遇伊拉克上校的最初片刻，目睹他令士兵在我们面前劫掠我们车里的物件，我们的生命似乎危在旦夕。 For the first few moments, [confronted] by an Iraqi colonel who had his soldiers loot our vehicle in front of us, it seemed as if our lives hung by a precarious thread. http://dict.cn/search.php?q=%E9%81%AD%E9%81%87

遭遇一般是客观的事物，多用于书面语，比如遭遇暴风雨，遭遇金融风暴等 经受一般是人的主观意识，多用于口语，比如经受失败，经受打击等。

经受，比较少用。一般为贬义词，形容遇到打击等。 遭遇，为中性词。如遇见某人，遭遇灾害等等

遭遇 zāoyù 1.[encounter (meet)with]∶碰上,遇到 遭遇明主。——南朝梁· 丘迟《与陈伯之书》 2.[lot]∶经受的事情;生活经历 亲身遭遇 经受 jīngshòu [stand] 承受;受到 他经受了严刑的考验 总的来说经受只有动词性质, 而遭遇则可作名词亦可作动词,一切要看语境.