"Sameness" by definition, is a loss of diversity. The theoretical advantages of sameness are many, although I want to emphasize that these are theoretical and seldom work out very well in practice.
In The Giver, as I recall, people have all the same material possessions and housing. The advantage of this is that envy and dissatisfaction should not exist. This is meant to promote peace within the community, since no one is going to need to think about the possibility that someone else has more, and no one is going to strive for more, if there is no "more" to strive for. This is meant, theoretically, to keep people happy, and it also conveniently makes them easier to rule.
There is also sameness in emotions in The Giver. This is, of course, achieved with drugs, since it would otherwise be impossible. But if everyone is at the same low emotional pitch all the time, again, because it keeps the peace. No crimes of passion will be committed because there isn't any passion. No one will ever cause a scene. Neighbors will not quarrel. Families will get along. And, again, this makes it quite easy for rulers to rule.
Colors, or, rather, the lack therof, are the same in The Giver. This, too, reinforces the repression of envy or dissatisfaction. No girl is going to long for a pink prom gown if all the gowns are the same. No one is going to be upset if a neighbor paints his house purple if there is no purple. And of course, if there is no color, husbands cannot complain very much about their wives' home decorating projects.
What the sameness in the novel does, perhaps most importantly, is take away a need to make decisions. Some people would consider this an advantage, but I hope that those who read this wonderful book come to understand what a terrible disadvantage this is.