I like some of the answers that have been given.
In one of the quotes, it is stated that the website DITL.org is one of the most accurate sources for ship specs and general info. This is true...with the EXCEPTION of the Intrepid class. There are also other instances where there are factual misrepresentations.
On that website, it states the intrepid class has type 9 phasers. This is incorrect. Based of info from interviews and articles, including the article on the design lineage of the Intrepid class in Star Trek: The magazine, the ship should have type 10 phasers with a similar output to a galaxy class. The ship, according that article, was designed as a smaller counterpart with almost equal overall capability to the galaxy class, with the direct purpose of being more manuverable and easier to build.
Also, the Intrepid class has an extremely advanced warp core. Notice that you never see a central dilithium chamber? This is because, like the 1701-A, the entire warp core is lined with dilithium thus creating a swirl matrix that makes the entire warp core a matter/antimatter reaction chamber. This allows the Intrepid class' warp core to achieve far higher power output even though it is generally smaller than warp cores of the Galaxy class.
The torpedo launchers are also dual purpose...they can fire photon torpedo's or quantum torpedo's. Generally speaking the Intrepid class' also carry more advanced photon torpedo's, type 6 versus the type 4 carried by Galaxy class starships. The computer cores are also way more advanced, allowing the tactical systems to respond more quickly and efficiently, as well as allowing the Intrepid class to manuver quickly and way more accurately than a Galaxy class starship.
Also, in an episode of Voyager where Kim was playing his clarinete (or however you spell that.) and complaining about the sound accoustics, Lt. Paris specifically states in dialogue that the ship was built for combat. The ship, as described in the writers bible of Voyager, was a medium cruiser and explorer, and would thus have the abilities of a Galaxy class ship. To note, the designation of a ship has traditionally nothing to do with firepower, and only size. The Federation usually groups the two togther though.
It should also be said that Voyager went up against the tactical cube with only a ruptured port nacelle and some hull breaching. Granted the crew probably had inside information from Seven, but even in that case it had a greater survivability than the Enterprise-D did against a regular cube. It might've been bigger, but it was also not a tactical cube. Voyager was able to get away and function without much repair time, where as the Enterprise-D cut sliced and diced and had to undergo weeks of repairs and refits.
In addition to that, the USS Voyager was able to withstand a year of hellish punishment at the hands of Anorax in the episode the "Year of Hell." The Voyager seems to have a similar level of survivability to that of a Galaxy class. Also, the USS voyager was able to flye in between two binary nuetron stars with its shields intact, though it did suffer from some damage as a result. This indicates strong shielding systems, especially considering it was trapped in a black hole. To be mentioned, the USS Voyager was operating on limited resources and no outside help, and was still able to accomplish what it did and then some.
Lastly, Admiral Ross's personal flagship was the USS Bellepheron, an Intrepid class starship. It is extremely unlikely that an admiral would choose a ship relatively weak in combat strength during a time of war, and that also indicates the Intrepid class is a lot stronger and greater in general ability than most give it credit for.
In a battle, i think an Intrepid class and Galaxy class would be a more or less even match, with the Intrepid class eeking out in manuverability and speed over the Galaxy class.