A good try, but I don't think so. Kruge openly says in TSFS that the old Constellation-class Enterprise outguns their bird-of-prey "10 to 1."
Thanks to sloppy reuse of the miniature and stock footage, it's since become established that there are two different sizes of BoP that inexplicably look exactly identical despite being built on two entirely different scales. The smaller
B'rel class holds about a dozen personnel and is the type seen in TSFS. The larger
K'Vort class reportedly hold a crew of 1500 according to the
DS9 Technical Manual (though I'm aware that's a controversial work) and is presumably far more powerful in its armaments. It's a silly idea that there are two different sizes of BoP, but it's kinda necessary given that TNG and DS9 generally treated the BoP as a much larger ship than TSFS did. (I wish they'd just used the
K'tinga miniature instead. That's a beautiful design, while the BoP is an eyesore.)
Now even assuming a more advanced bird-of-prey, the Galaxy-class Federation flagship eighty years later should indeed be armed to the teeth and be even MORE of a mismatch with the BOP than it was previously, or the Feds are run by incompetent morons.
Or Starfleet was run by people who had other priorities than killing things. It's a fundamental mistake to assume every Starfleet vessel is a battleship. That may be a valid way of thinking of the ships that were built after Wolf 359 or during the Dominion War, but it doesn't reflect the real-world philosophy of the people who developed TNG and designed the
Enterprise-D, and thus it doesn't reflect the in-universe philosophy of Starfleet at the time the
Galaxy class was designed and created.
You don't lightly arm the jewel of your fleet.
No, but I'm not saying it's simply a matter of how many weapons a ship has. That would be a gross oversimplification. Even TNG's developers, working on the assumption that they were designing a ship of peaceful exploration, nonetheless made a point of establishing that it had formidable defensive armaments. Nonetheless, it stands to reason that Federation starship designers thinking of exploration first and seeing defensive combat as a necessary evil might not design ships that were as robust under combat conditions as Klingon starship designers who intend their vessels to be super-tough, macho killing machines and nothing else. It's not a question of relative firepower, it's a question of generalization versus specialization. If combat is the only thing a ship is made for, it stands to reason that it would be better at it than a multipurpose starship whose combat capabilities are geared toward defense and intended as a last resort.
They also have MORE of a reason to be heavily armed than earlier Federation ships because Enterprise-D has families on board.
But weapons aren't everything. It's not just a question of how hard you can hit, it's a question of how well you can take a hit. It doesn't matter how formidable your right hook is if you've got a glass jaw; a weaker opponent who gets in a lucky hit can still take you down. The E-D wasn't defeated because it was outgunned, but because the enemy found and exploited a gap in its defenses. This was what I intended to suggest above by pointing out the poor survival rate of the
Galaxy class as a whole. I was suggesting that maybe the design has a glass jaw, that perhaps it wasn't made as robust and resistant to damage as it could've been.