As a native Korean, X(으)로부터 feels like that a certain event or object originates from, arises from, or occurs because of X, whereas X에게서/한테서 feels just like the plain old English word 'from' with slightly limited usages.
- There are many views that says the recent subprime mortgage crisis occured because of the prevalent moral hazard in the financial industry. (최근의 서브프라임 위기는 금융 산업 전반에 걸친 도덕적 해이로부터 일어났다고 보는 견해가 많다.)
(도덕적 해이 - moral hazard; In this case, 에게서/한테서 IS NOT appropriate)
- This letter is from Stephen Hawking. (이 편지는 스티븐 호킹에게서/한테서 온 것이다.) (스티븐 호킹 - Stephen Hawking......obviously; In this case, 로부터 IS appropriate as well.)
Above was my personal view/interpretation of the words, and the link is the official answer to a similar question from National Institute of Korean Language. (http://krdic.naver.com/rescript_detail.nhn?seq=7486)
It basically says that (으)로부터 can be used with both people/animals and others (plants, other inanimate objects, events/concepts...), while 에게서 is only used with the former.
It also says the more traditional usage is to use 에게서 instead of 로부터, and 로부터 is being used more often nowadays because of the influence of the English word 'from'.
Although I cannot state categorically that 로부터 is more generally/broadly used, I hope this answer helps.