And with the warp speed effect using the Q-flash instead of the cartoons streaks suggest substantial changes to their warp systems.
...Alas, ENT then shows that the Q flash "always" was part of the warp technology. And then ST:NEM showed that warp engines can have contrails (this time of smoky nature) despite having the flash. And the alternate timeline sort of has the flash, even if it isn't of the exact shape of the Q finger-snap any more.
Perhaps the difference in warp visuals is not a matter of technology (since we've seen Klingon and Jem'Hadar warp from "inside" and "outside", too, and it looks the same as contemporary Federation warp), but of vantage point? Perhaps you see TNG streaks when the camera is at a certain position vs. the warp field, but TOS/TOS-movie stars when it is at another position - and rainbow contrails when it's at standstill and the ship wooshes past, but no contrails when it follows alongside the ship?