The new films *do* have standardised warp factors. When the Enterprise is at maximum warp the viewscreen infront of Sulu and Chekov reads Warp 4.25 twice during the movie.
I thought the maximum velocity was warp 7, or something. I did see that somewhere, I'm sure, so hearing warp 4 in the movie I thought it was a bit slow to catch up to a ship from the later 24th century.
And in TOS "The Enterprise Incident" Kirk orders warp 9 for, I think, the only time of the series.
This is also after Enterprise has taken a pounding on arriving at Vulcan. Damaged ship not as fast as undamaged ship - seemples.
A pounding ? It was hit once.