I think both have the same meaning. One is a adverb the other is a verb perhaps. 我想它们都有一样的意思， 一个是形容词别的是动词 adj. pitiful :可怜 verb to be pitiful: 怜悯 请怜悯我吧，告诉我她的名 For pity's sake tell me her name. 我觉得他很可怜 I think he is very pittyfull. 可怜的你 pitiful you.

I agree with Chinese_Speaker_Hy. Additionally, in classical usage (poetry included) it can also mean 1. "to be admired" as in 白居易「姊妹弟兄皆列土，可憐光彩生門戶。」 2. "to cause sorrow/regret for somebody" as in 李商隱「可憐夜半虛前席，不問蒼生問鬼神。」 3. "to provoke love (because they are so weak, defenseless etc)" as in 李白「借問漢宮誰得似，可憐飛燕倚新妝。」 or杜甫「春草何曾歇，寒花亦可憐。」 4. How lovely as in 白居易 「可憐九月初三夜，露似真珠月似弓」 Hence the two terms are not interchangeable.

I would never say 憐憫 when I'm talking to someone.

First and foremost, 可怜 is much more colloquial than 怜悯。 Second，可怜(literally,deserve + pity(in ancient times,Love,though ) is either adjectival or (transitively) verbal. This means you can say: 他好可怜|| 可怜的小鸟被猫咪捉走了|| 可怜的样子（pitiful looks）. And also you can say: 我可怜他 怜悯（literally，pity(V.）+ pity(V.)) is only used in writting and formal language. And it is a verb, not adj.So you cannot say: ✘ 他好怜悯 ✘ 怜悯的小鸟被猫咪捉走了 Similarly, you can say: 我怜悯他 And you can say,怜悯的样子(pitying appearance)||怜悯的神色(pitying looks)---- Compare with 可怜的样子（pitiful looks）---- The difference comes from the elements(morphems) and their constructing modes.

roland is quite right but still a bit wrong 可怜can be动词 too 我可怜你 most of the pity can use as 可怜 怜悯is verb but only few situation can be used 怜悯 we seldom use怜悯in talking but it used in poem or essay more than可怜