Unmarried parents with 2 children. Can we claim one child each or do i have to claim both?

IF you live together and both are the parents of the children you can each claim one or both as long as one particular child is not claimed by both of you.  If each of you claims one, one of you can file as Head of Household if otherwise qualified, and the other would file as single.

would this be beneficial in some way for each parent to claim one child rather than one claims both?

Depends on your incomes.  Only by doing returns both ways can you see what would be better.