Hi, Left Frog here, consumer of the Baka Baka no mi.Shichibukai as primary antagonists.
Both are the first noteworthy antagonists of their section of the Grand Line, arguably being the gateway villains to said section of the Grand Line.
Both have taken over an island by using cruel methods of turning the people against their original King.
In both Arcs, the daughter of the King spoke and appealed to Luffy personally.
In both Arcs, there is a point where the heroes are momentarily victorious and it seems like everything will be better before one of the Shichibukai orders or performs an action that turns the people of the country on each other.
Many characters from both the Donquixote Family and Baroque Works have very similar Devil Fruit powers. For example, Senor Pink and Miss Merry Christmas have very similar Devil Fruit powers and so do Mr. 5 and Gladius.
There may be other similiarities but those will have to wait to be edited in later as either I'm too lazy to look for more or other similarities may be yet to come. Either way, you saw it here first (I hope) and I hope it gets you thinking. I'm the Left Frog, Baka Baka, have a nice day, bye.