First, we will get a damage boost, and depends on the weapon you might get a better range for the charge attack or even an ability to inflict status,
as we upgrade up our swords and guns
As a general rule of thumb, the bombs get a larger blast radius when we upgrade them.
Now, let us ask ourselves, what did the "new" shard bombs gain when we upgrade them?
the answer is higher damage.......hummmm......the whole reasoning behind changing the old shard bomb was to stop it from being "not very bomb-like." however, they have turned this into more sword and gun like behavior by not awarding these shard bombs a larger blast radius.
I think its more in how they function and less in what happens when you upgrade them. There are other major flaws to them, I wrote a guide in the suggestions forums if you are interested.