It's the same exact show.
But your perception of it is changed (well, I'm guessing, I've only seen frames of TNG on BR.) I assume the difference is probably something akin to seeing excellent VHS tapes from 35mm on TOS in the mid to late 80s in place of a decade of 16mm versions in syndication, which for me was a revelation almost on par with seeing TOS on laserdisc and later on DVD.
It's not always a good thing ... when I saw the crisper ENEMY WITHIN, I was badly distracted by the makeup on evil Kirk.
But by and large seeing more detail and with greater clarity improves the experience. Look at BLADE RUNNER on widescreen VHS (yeah, I actually work with somebody who only has movies on VHS) and then look at it on BLU-RAY and yeah, it's the same movie but such a different impact, the BR gets you back to how it looked in the theater (and I'm guessing when they get around to releasing 2001 in 4K it'll be the same trip back in time for me.)