Star Wars tends to use the word “blaster” for anything from handheld pistols to light point-mounted machine guns, and “laser” for basically anything larger, from the main guns of an X-wing to the main gun of the Death Star. So I’m approaching Star Wars lasers as intense beams of photons. Other weaponry exists in the Star Wars universe but I don’t believe the Death Star have any, such as the “ion cannon” that stun locks a star destroyer in Empire Strikes Back.

I haven’t the vaguest idea what “phasers” actually are. The Star Trek universe also contains lasers, at least once Worf says “They’re firing lasers at us, sir” to indicate an opponent is pathetically outclassed by the Enterprise D, also “disruptors” seem to be a competing technology. So I think the Borg would be able to adapt to Star Wars energy weapons, they’ve likely been exposed to multiple types of energy weapons.

I imagine the Death Star’s TIE fighters would be completely ineffective against the cube; Star Trek phasers seem to have a much longer effective range than most Star Wars lasers and blasters, so they’d be shot out of the sky before even beginning to engage.

I’m basing the estimates of speed on language alone; they often refer to ships in Star Wars as jumping “to light speed” which, yes, on a galactic scale is hilariously slow. I don’t think we ever see a hyperdrive journey in real time; but for example during the trip from Tattooine to Alderaan(s debris field), Han and chewie are hanging out in the passenger compartment with Luke and Obi Wan passing the time. There may have been hours or days trimmed from this trip. And the Millennium Falcon is established as the very fastest ship in-universe, the Death Star is capable of hyperdrive but not particularly fast. Borg Cubes in their universe are capable of easily outrunning even the fastest Federation ships.

The Death Star’s planet killer laser: It is shown in Return of the Jedi firing an underpowered shot to destroy one of the rebel capital ships, so at least the second Death Star is capable of accurately tracking and hitting starship-sized targets. It’s established to the point of cliche that if hit with enough power, Star Trek shields can be overwhelmed to the point of failure. So that raises these questions: Can the Borg adapt to a reduced power shot calibrated to destroy the cube’s mass? Would their shields, even if adapted, withstand a full power planet popper shot? Would the crew of the Death Star decide to use full power on such a small target before the Cube closed to transporter range? Would they have time to fire a low power shot, see it not work, recharge the laser and fire a full power shot?

The Borg have basically no hope of significantly damaging the Death Star; it’s so huge that it’s capable of just tanking a collision with a super star destroyer, their play here is boarding and assimilating.

Also, I want to change my earlier answer: Daniel Jackson doesn’t die twice, he gets assimilated. Then the Borg Queen tries to do some weird psychological power play with O’Neil by showing him Drone Daniel, but Teal’c shoots the Borg queen with a Zat gun, which they haven’t used at all the entire mission so the Borg aren’t adapted to it yet. O’Neil pulls a tube out of the stunned Queen’s head, she screams and dies, Carter configures the Naquadria to detonate their main core or whatever on an Alienware laptop the Air Force issued her for some reason, Drone Daniel is hunched over because of the death of the queen, they take him to the Tok’ra, Tollan or Asguard to get him fixed depending on what season it is. Episode ends in the SGC conference room with General Hammond saying “Who knows how many of them are still out there?”