그는 그의 삶을 포기하기를 원했습니다. 그는 그의 삶을 포기하고 싶었습니다. They have the same meaning. And there's no difference in these two sentences. I think the difference of nuance is silmilar to Egnlish "I want, I'd like to" , you know it's different with Englsih but a bit similiar. 원하다 = want -고 싶다 = I'd like to , I feel like(:when it means you want something) -고 싶다 ' is used generally, Usually we don't use '원하다' colloquially in personal and slight desire. ex) 나는 밥 먹고 싶어요. >> 나는 밥 먹기를 원하다 (It's correct but usually we don't say like this way. But sometimes we use it, when emphasize what we want. ' 내가 원하는 것은 당신입니다.' ) And when you have an object(opponent), you can't use "싶어요" '싶어요' is only personal desire. ex) I want you to come with me. 나는 당신이 같이 갔으면 좋겠어요.(most generally used ) 나는 당신과 같이 가길 원해요. 나는 당신이 같이 갔으면 싶어요(A few people can say this, it's too passive speech way. And I'm not sure this is correct grammatically and even if it's correct, usually we don't use in writing. ) And for instance, a supervior could send you a message or an email officially, 저는 빨리 당신의 보고서를 보길 원합니다. I wan't you see your report quickly. It's ackward to use' 봤으면 좋겠어요' in this situation, it's too freindly. (Although a supervisor would prefer to say this. "빨리 보고서 제출하세요") Basiclly they have the same meaning , and what I wrote below is just tendency, not extact distinguishment. -고 싶다 : generally used, personal and instant desire. 원하다. : when you want to emphasize what you want, having more strong desire, a dream of future, in writing. etc I hope this is helpful for you :)

Hello~ before I start explaining the differences between the two sentences, I'd like to correct them first. "그는 매우 좌절했기 때문에 그는 그의 삶을 포기하기를 원했습니다." "그는 그의 삶을 포기하고 싶었습니다." The words, "하고싶다", "원하다" are the same. But "하고싶다" is more active and widely used. Ex) 노래 하고싶다. = I want to sing. 노래 하기를 원한다. = I want to sing.