To me, a big difference is in the lengthy prelude, which follows the model of TOS, just with an updated production. First the synths layered with strings, which are very 80's wonder-music(it could be right out of the score for Flight of the Navigator or The Goonies) and then the french horns come in playing a round, which adds a Wagnerian element.
The percussive "march music" elements quoting TMP are subdued in TNG's arrangement - it's a less compressed, "punchy" sound, and I believe the mic has been set farther back or they've EQ'd out some higher frequencies. Those decisions, plus a few choices of instrumentation like the harp glissandos, tone down the bombastic energy and add a gliding, romantic quality. Again, more like TOS, but updated.