I notice that someone is making the mistake of quoting the wrong stats when telling people about the maximum warp capabilities of the Enterprise E. Maximum warp capabilities of the Enterprise E sits at warp 9.999. The ship was built 'after' the Voyager. The major mistake they make is this...it is clearly stated that the 'sustained cruising speed' is Warp 9.999...which means that the Enterprise E is capable of traveling at this speed indefinitely. Even these numbers are rounded off though...meaning they are incorrect...as you can actually find the technical readouts in the TNG technical manual. This gives the Enterprise D a max Warp of 9.9999. Considering that Warp speed ratings are also exponential...that 0.0009...is a huge increase in speed.
The answer here is actually much simpler that many think. As long as the Scimitar was capable of traveling at warp factor of 0.00000000001 faster than the Enterprise E...it would have overtaken it since the mathematics is, as stated, exponential.
We should also remember that, since the Enterprise E was built after the Voyager was lost (Voyager was lost in the year 2371 and the Enterprise E was built in the year 2373...one year before the events of Star Trek: First Contact)...in this case...all the technology available at the time that Voyager was built with was technically available for the construction of the Enterprise E. 126
There is no reason to believe that the same tech wasn't used to build both ships. The Voyager then returned to Earth in 2378...events of Nemesis took place in 2379. It is plausible that all outfitting took place after the Voyager returned. All new tech available was likely scheduled to be refitted, first and foremost, for the 'Flagship' of the fleet. I mention this because of the fact that <PERSON>...this is documented in the show...created a Warp vessel capable of reaching Warp 10. So The Enterprise E would have been, easily, as fast or faster than the Intrepid and the Prometheus Class ships (built in the mid 2370s).
It is also confirmed,...The Enterprise E underwent the actual refit about a year before the events of Nemesis as well...so it stands to reason that, while more weapons were added...a new, faster, warp drive was installed as well. This would make the 'E' just as fast (at least) or faster that the speeds stated by other commentators.
Timelines are very important in a question like this...technical readouts are another...one cannot just read out of date information to make claims about conclusions.
The issue with this is that the max Warp speed of the Scimitar, by all available sources, is actually 'unknown'...but does have a Warp rating of at least 9.7. We cannot assume that the Scimitar is fast, nor slower, that the Enterprise E based on any given data anywhere. We just have to take it as fact that it is faster though....because that is what is shown to us in the movie. 126