I wouldn't really agree that Littlefoot has less responsibilities than the others. One might think so because of the absence of family members other than his grandparents, but maybe Littlefoot is seeking responsibility more than any of the others does.
We saw Littlefoot taking responsibility for having not taken responsibility before in LBT 11. He felt very much responsible for Chomper in LBT 2 and (as far as the situation permits this expression) in LBT 5 as well. In LBT 4 he feels it is his responsibility to prevent the death of his grandpa, in LBT 6 he wants to shoulder the responsibility for some strokes of badluck (which he feels has been caused by their damaging of Saurus Rock), in LBT 7 he is one of the main voices (though Spike is the one to make the ultimate decision for everyone) to follow Ducky (taking the responsibility the grownups seem to be unable to take on quickly enough) and in LBT 9 he feels responsible for Mo and his presumed death. These are not all examples I think, but looking at them I would not say that the absence of family members other than his grandparents results in Littlefoot having less responsibilities than the others. To some degree he may be one of those characters trying to shoulder all the responsibilities in the world sometimes not realizing that he need not take all the weight of the world just on his own shoulders.
In case of Littlefoot I would agree that we see less scenes of him shouldering responsibilities. He does to some degree in LBT 5, but most of the time his peculiar situation puts him in a position that differs somewhat from that of any of the others.