As for "faster or not?", we have a nice benchmark in that an Enterprise flies from Earth to Vulcan in two universes. In ST:TMP, Scotty says it will take four days. In the 2009 movie, it takes however long Kirk sleeps under McCoy's sedation, plus the time he spends running the corridors of the vast ship, disoriented, before reaching the bridge and arguing with everybody for a couple of minutes. But no longer than a single day, as Chekov in a PA refers to events preceding the launch and yet taking place within 24 hours (or else he would need to specify that the hours he quotes in Zulu Time format refer to some other day altogether).
Is the 2009 ship four or perhaps ten times faster than the 1979 ship? Apparently so, on this stretch of travel. But the 2009 ship is in a real hurry, while the 1979 ship was ferrying a passenger after a ship-straining ordeal and was yet to perform a proper shakedown. Emergency dashes are entitled to being ten times faster than cautious cruising, I guess.
We have few other points of comparison. In ST:ID, it's also less than a day to the Klingon border and back, the first leg being at stealthy cruising, the second at all-out, monsters-on-our-heels emergency dash. But the Klingons were close in ENT already, and lamentably the TOS timeline ship never performed this exact journey on screen, for our comparison comfort.
Timo Saloniemi