The NX-01 would most certainly NOT out fight or gun the Enterprise-D, or for that matter ANY Galaxy class starship.
Well, aside from the fact the Enterprise didn't have the greatest sheilds as they were in the infancy stage of that technology, they didn't have advanced weaponry at all.
Going by the century, phase canon's pre-date TOS' lasers. I'm assuming that phase cannon's were a particle laser weapon of some sort that gave birth to the lasers used by the Constitution class. Or, i like this one better, phase-cannon's proved too taxing or not as reliable as the lasers created later on. perhaps Starfleet could focus more energy into a Laser than they could a phase-cannon. Phasers rolled around once lasers were maxed out on power, and using the lessons learned from Phase cannons starfleet was able to create a much more flexible weapon.
Photon torpedo's....Well, a photon is a light particle. The term photon torpedo only refers to the fact that it emits light as it travels to the target. The photonic torpedo simply does the same thing. However, both are stated as antimatter weapons so there in lies the rub. I offer a possible explanation.
Photonic torpedo's could be an ancestor of the more modern photon torpedo which entered service in around 2245. If people will recall, the photon torpedo was initially a slow, short range weapon that you could even outrun if you were quick enough. That said it's possible that yes indeed the photonic torped worked in much the same way, but engineers couldn't get around the range to explosive yield ratio (remember that to travel the torpedo uses it's own warhead for fuel.), and thus abandoned it in favor of the more flexible and longer range nuclear warhead, which they still could make yet even more powerful.
This all said, going by the timeline, Enterprise's weaponry and defensive capabilities were much more primitive than a Galaxy class weapons.
Photon torpedo's by the 24th century had a maximum range of 4 million KM with a payload of 1.5 kilo's of matter and antimatter, with a stock compliment of around 200 torpedo's with industrial replicators to make mroe. The type ten phasers used by that class of ship had an output of 50 TW (initially MW, but that would be underpowered and Voyager repeatedly used the TW range, and Intrepid class ships have type ten phasers as well.) PER SEGMENT. The dorsal phaser array of a galaxy class ship has over 200 emitter segments, most of them working in pairs.
The galaxy class starships shields are also extremely strong, though in the 2360's not as strong as an Intrepid or Sovereign class'. This assumably changed with the outbreak of the Dominion war. The Galaxy class has some 12 heavy sheild generators littered around the ship not counting backups or ones used in separated flight mode. In addition to on board firepower and defensive capabilities, the large shuttlebay on decks 3 and four can comfortably carry squadrens of shuttles with their own weaponry.
All in all...
the galaxy class ship would own the NX-01. Simple. Whether it is beaten down with shuttles and the ship itself, or destroyed because the Galaxy class separated and fought with two ships, or by the fact that the Galaxy class' weaponry has a longer range than anything in the 2150's.
It's also worth noting that the warp core of an NX class starship doesn't even havea highenough power output to maintain anything over warp 5 and is TINY. The galaxy class warp core occupies 10 decks, and can maintain a cruise velocity of warp 6 indefinately, with an emergency speed of warp 9.6, and by the time of the dominion war warp 9.9.