A family floater policy is the one in which the entire family shares the sum insured for the policy period.
For example, imagine a family of husband, wife and two kids all insured under the same family floater policy. Their total sum insured is 5 lacs. If the husband is hospitalized for a cardiac surgery and the hospital bill comes up to 3 lacs. The entire family is left with the coverage of 2 lacs for the remaining policy period. If one of the kid falls sick with dengue in the same year and draws a hospital bill of 1 lac then the sum insured goes down by another lac Rs.
Hence, it is quite obvious. If the family is less likely to fall sick a family floater is great idea as the sum insured is hardly going to be utilized. However, if the probability of the family falling sick is high then family floaters are not recommended as the entire family will need to bear the brunt of a single hospitalization of high amount.
The choice is easy. Family floater policy for a healthy family and individual policies for a family with serious medical history.