This is kind of silly. The ship can do whatever the writers make it do in that episode. Every Trek ship could beat any other one depending on the story.
I'm sure if the NX-01 met the Mirror Universe Enterprise -E it would find a way to beat it....because in this instance the NX-01 is the hero ship.
Use some common sense will you?
We are talking about 2 ships that are 200 years apart in terms of technology.
The Enterprise-D would be vastly superior to NX-01 and the rest of the Alpha quadrant of the mid 22nd century, and would be able to engage fleets of those ships and still come out on top (if MU episode of Enterprise is any indication, the 23rd century Constitution class 'Defiant' was safely protected by shields at all times even when it was under a barrage of more powerful 'warships' from Andorians and Vulcans).
The Enterprise-E doesn't even exist in MU from what we know, so i won't even commend on that one.
Yes, your point that the heroes do whatever the writers set them out to do is pretty much accurate ... but you yourself know that we are talking about writers that have issues merging highly advanced tech to work with drama (so they dumb the tech to make the drama flourish, which often fails and ends up insulting people as well).