Most of the contact the Federation has with the Borg happens before DS9. And Voyager has tons of Borg contact because it’s in the Borg-controlled quadrant of our galaxy, while Deep Space 9 resides far from active Borg space.
In late 2366, a Borg cube invaded Federation space and assimilated Jean-Luc Picard, whose tactical information contributed, along with the Borg's own vastly superior power, to Starfleet's disastrously one-sided engagement with the cube, the Battle of Wolf 359. A fleet of forty starships assembled to combat the cube. All but one of these ships were destroyed, while the cube remained intact, damaged but healing rapidly. The Enterprise-D recovered Picard and used his connection to the hive-mind to disable the cube before it could attack Earth. (TNG: "The Best of Both Worlds", "The Best of Both Worlds, Part II")
We witness some of this event in DS9: this battle is where Sisko's wife dies.
During the next few years the Borg face major set backs in the Delta quadrant; this is witnessed by the Voyager crew.
The next major incursion by the Borg into Federation space happens in 2373 (in the TNG movie First Contact) — the same year the Dominion War happens, a major plot theme in Deep Space 9. And as Richard states, this Borg attack is centered directly on earth, far from the Dominion War and Deep Space 9.