As suggested in the following extract bemoan is a transitive verb whose object is generally an abstract concept (absence, lack, failure etc.) while moan is an intransitive verb:
Bemoan is one of a group of English verbs starting be-, where the effect of the prefix is to turn an intransitive verb into a transitive one. So to wail is to cry out in pain or sorrow, while to bewail something is to complain strongly about it. Bemoan fits with this pattern:
to moan is to complain, and to bemoan something is to complain about it. The ‘something’ is important: typical objects of the verb are nouns like ‘lack’, ‘dearth‘, ‘absence’, ‘decline’, ‘failure’ and ‘loss’, along with ‘fact’.
You do not usually bemoan people, yet the other day I saw someone hoping she would not turn into ‘a decrepit old woman bemoaning young people with their whole lives in front of them’. The writer seemed to be using bemoan to mean ‘moan at’ or even ‘nag’, rather than ‘complain about’. I haven’t yet seen this meaning used widely, but it will be interesting to see if it catches on.