Honestly, I disagree. The shields may adapt, but you're still talking about a weapon made to destroy a planet being pointed at something that's maybe 4 or 6 times the size of a star destroyer (don't really fell like calculating that precisely, but memory alpha lists the cubea as roughly 3 cubic kilometers while a star destroyer, from memory, is about 1.6 kilometers long and much less for height and width; for comparison, the first death star is listed as 120 kilometers diameter and the second as 160 on wookieepedia)

I think a better head-to-head would be a Borg cube vs a super star destroyer like Executor (8 kilometers length, powerful but not planet cracking weapons)

It's like if the Enterprise were to shoot phasers at a single drone on the ground. I don't care how much those shields adapt, that's simply too much raw power for a shield generated by a humanoid sized suit and set of implants. I don't remember specifics but i vaguely remember at least one instance in Star Trek where they managed to overpower a Borg's shields. They are not perfect, no matter how good the tech is it still runs on energy and it still uses energy to absorb energy.

And for my biases: I love both, but I've always had a preference for Star Trek. My opinions on this aren't based on a preference for Star Wars at all.