this is gonna keep going because fan boys refuse the truth,its too hard for them.
lets try and make it realistic as possible.
1-Shields : Intrepid are clearly more advanced(10years) capable of protecting the ship not from heavy fire but from many anomalies as well(''Scientific methode'' voyagers massive shields protected it inside 2 superstars)(''think tank'' Voy Shields repelled all damage from an Exploding planet,then protected the ship from a huge gas eruption)in addition with a mark9 warp core an intrepid can produce more power to go faster(warp 9.975) and reroute more energy to shields if needed.
2-Hull : Hull integrity is determined by 3 factors overall Volume,armor,structural integrity fields.
Volume goes to a Galaxy with X5 times the size of an intrepid.
armor is the same on both these classes.(unarmored)
integrity field clearly goes to Intrepid after what Voyager suffered in year of hell and kept going i think its not so hard for any person with a brain to admit that,and i recall so many times in TNG a few blows to the hull and captain warp core is overloading the ship is gonna be destroyed lol (USS Yamato,Odyssey,Enterprise D...list goes on)
But with 5 times the hull volume i will be more then enough to match it.
Phasers : Galaxy class 11 arrays Intrepid 14 arrays,clearly intrepid wins.
something that people also should consider that we barely saw the galaxy firing more then 2 arrays at once while we have seen on screen the intrepid fire a lot more simultaneously.
Torpedoes : Intrepid 4 launchers Galaxy 2 Launchers in numbers the advantage is for intrepid.
Compliment: Galaxy wins this without a contest 250 is a huge amount,while the intrepid considering its volume only have 50 at its disposal.
Warhead types : Galaxy is limited to mark4-5 photon torpedoes while an intrepid has mark6 and mark9(heavy yield)
as well as spatial charges and tricobalt devices capable of making a tare in subspace far superior firepower but very small supply of them.
Weapons wise the quantity and effeciency in long battles or multiple battles goes to the Galaxy tho quality wise and instant and fast assaults the advantage goes to the intrepid.
do not post idiotic stuff like Galaxy class has larger arrays=more power,that was never stated on screen and people tend to forget that so many tiny ships produce far more firepower then large ones in trek universe like the Defiant or species 8472 bioships.
impulse engines : <.< not even a contest Galaxy in most battles is a slow as a snail,usually stationary in combat.
Warp speed : very fast ship warp 9.6 max
impulse engines : very fast and highly maneuverable only Federation starship that can maneuver the plasma storms int he badlans...we even saw the ships out-speed theta radiation wave at impulse etc...
Warp speed : uber speed warp 9.975 fastest federation starship on record before the Prometheus class.
All that i stated in on screen evidence and cannon,if want to argue try doing so with something genuine not stupid and illogical.
The Verdict :
Intrepid : Shields : 9/10
Hull : 6/10
Speed : 10/10
Galaxy : Shields : 7/10
Hull : 8/10
Speed : 6/10
those are the factors i think you should consider when comparing strength between ships in trek.