Well, I have sailed on both ships (the Dawn Princess several times).
I think that the cabins (I have not done checking, but from my observation and usage) on the Coral Princess are larger.
I have seen childrens activities on both ships, seemed equal to me.
Now....alternative dining on the Coral will be better, in addition to the dining room (traditional or personal choice), you have the buffet, Bayou ($10 pp cover charge) and Sabitinis ($25 pp cover charge)...both the alternatives on the Island Princess (did not do them on the Coral Princess cause MGram wouldn't let me
) were OUTSTANDING.
As for a cabin for 4, a 'normal' (non-mini-suite or suite category) will be 2 lower beds and 2 bunks pulled down from the ceiling.