ci viene addosso
viene addosso a noi
are “grammatically equivalent”, but not strictly “semantically equivalent”. The pronoun ci has the same role as a noi, but it's a question of emphasis. Similarly for gli which stands for a lui, a lei or a loro.1
With gli è caduto il ramo addosso the emphasis is on the person who’s hit by the branch, rather than on the branch; to the contrary, il ramo gli è caduto addosso would put more emphasis on the branch. A third form is possible: il ramo è caduto addosso a lui would convey the idea that the branch fell onto him and not other people.
Similarly, viene addosso a noi could imply that it came against us and not other people.
Nuances, but they're important. I'd say that ci viene addosso would be the preferred form unless a particular shift on emphasis is needed.
1 Prescriptive grammars may say that gli for a loro is an error; they're contradicted by many authoritative writers and speakers.