In Galaxy 2, if I tilt the analog stick all the way, Mario is at top speed in like half a second.
In 3D world, if I tilt the stick while holding the run button, Mario doesn't reach top speed until the dash kicks in, which takes a second or two. I've gotten hit, or died, often in 3D World because the dash kicks in at inopportune times, during precision platforming, when surrounded by enemies, etc.
If it was a 1-stage run, where you're either running or not, it wouldn't be as problematic. But since the 2nd stage of the run button doesn't kick in until you've been running for a short time, you can't decelerate then accelerate to max speed in a pinch, which diminishes the precision you have.
Through my playthrough of 3D World I found myself running in circles on "safe" platforms just to get the dash to activate before preceding through the level.