Hiyas
Well first off, Balloon Berry only works once, and then it is discarded. Fluffy berry is a more permanent thing, and remains attached until your pokemon gets Ko'd or it evolves into an-ex, etc.
Secondly, Balloon Berry can be attached to pretty much anything except for pokemon that already have tools on them. Fluffy berry differs because it can't be attached to ex, dark pokemon, or pokemon with owners in their name.
I'm not sure which one is better. If you have a fluffy attached then you can no longer use Strength charm/Crystal shard on that pokemon.
~Secretsmeargle