As an exploration ship, the Galaxy class was a success - the Enterprise's accomplishments are proof.
From a military POV, the galaxy was an embarassment. The warp core was vulnerable, the nacelles were vulnerable, the power system was vulnerable, etc
In DS9:Way of the warrior 2, The Defiant (without shields) withstands fire from a kingon ship (considerably larger than a BOP) for minutes, and is in pretty good shape afterwards.
The Defiant also used it's tractor beam to deflect the incoming fire from the Klingon Vor'cha class battle cruiser. The Defiant then relied heavily on its thicker armor to wistand the hits that came through. Sisko had wanted the Cardassians to follow him and warp out, but the Cardassian ship was a wreck. He took a chance. He was lucky.
In VOY:Equinox 2, Voyager survives fire from the Equinox (whose crew knew voyager's shield frequencies) for minutes and is in pretty good shape afterwards.
Equinox was heavily damaged herself, by both Voyager and the aliens. With 4 torpedo hits Voyager lost, weapons and impulse drive and had hull breaches on deck 4.
Link. A pretty good showing, against a science vessel. Equinox fired 4 torpedoes. 1701D was hit by much more. Older vessel or not, it was hit much more and had little room to maneuver.
In Generations, Enterprise is destroyed by an ancient BOP (who knew its shield frequencies only at the beginning of the battle) in minutes. Pathetic.
Most likely, the Duras Sisters knew the shield frequency throughout the battle. I gave my reasoning earlier in this and another thread.
In TNG:Cause and Effect, an old federation ship strifes enterprise's nacelle. Enterprise blows up less than a minute later.
The 1701D also had lost lost main power BEFORE her nacelle was hit. Without that she was a sitting duck, unable to really do much.
In DS9:The Jem'hadar, both the Federation and the Dominion wanted to prove its strength to the other party. The feds decide to send a galaxy class - with predictable results: an embarassment for the federation.
Federation shielding was useless against Dominion weapons. Keogh made what, at the time, seemed to be the right call. He dropped shields and put that power to weapons. The Odyssey lost her targeting systems and power to weapons and her port nacelle was venting plasma. The Jem'Hadar ram the Odyssey right in her engineering section. Could any ship survive all of that? Until she was rammed, she was holding together.
In DS9:The Search, The Defiant did much better than the odyssey.
The Jem'Hadar weren't out to destroy the Defiant, but to capture it and its crew. There is no reason to believe the Defiant would have survived had the Jem'Hadar been ordered to destroy it.
And then there are, of course, the numerous episodes where enterprise's power grid or warp core seem to want desperately to fail, and do so as often as possible.
The Naked Now - The crew disabled the 1701D
The Last Outpost - Superior technology disabled the 1701D
Home Soil - The silicon life forms were able to take control of a limited portion of the ship and computer.
Elementary, Dear Data - Moriarty was the ships computer.
Contagion - Alien "Virus" much more advanced than the 1701D computer caused the problems.
Evolution - Nanities infest the 1701D
Booby Trap - The name says it all.
Yesterday's Enterprise - 1701D overpowered with little room to maneuver.
Tin Man - Alien creature disables the 1701D and destroys a Romulan Warbird.
Hollow Pursuits - Nearly ship wide contamination caused the problems.
Galaxy's Child - Alien creature "feeds" off the 1701D
Night Terrors - Power loss caused by the rift.
Disaster - 1701D collides with quantum filaments, computer was not completely functioning.
Cause and Effect - explained above.
Timescape - the Aliens sent a feedback loop that overloaded the warp core, only the time bubble saved the 1701D
All Good Things... - The anti-time distortion caused 2 of the 3 1701D's to blow up.
I think those are all the times the 1701D lost power or her warp core was ready to blow. That's less than 10% of the episodes.