Maneuverability also plays a role. The Defiant and Intrepid classes seemed to be much more maneuverable than the big Galaxy and Sovereign classes. Their shields could have been less powerful, counting on them being able to dodge and weave, allowing more power to dumped into the phaser arrays. The Sovereign class 1701E, in battle with the Scimitar, also suffered a large physical blow from a chunk of the Romulan ship which was blown away. Geordi had to restore the shielding to the bow to help keep the 1701E in the battle. In my opinion, in the interest of speed he diverted power from the other shields, to even out the shield power (They never really knew exactly which direction the Scimitar would fire at them from) to protect the ship. That allowed the Scimitar to open a hole in the shields so the Reman strike team could beam aboard.
As for phasers I think Yesterdays Enterprise put it best:
Castillo: What's a TKL?
Tasha: Standard rations. Food replicators are on minimum power, so everything else is diverted to defensive systems. So where was I?
A ships power output could be shunted over to shield and weapons allowing for the ship to have reserve power for weapons and shields. Ships like the Intrepids could have Type X phasers and put out full power because other ships systems were at minimum power. Voyager, for example, rarely used its replicators for their main purpose, feeding the crew, opting for a Galley to save power. During the war the Galaxy class were most likely only using Starfleet and specialist as crew leaving families back on their home worlds or space stations. This could have allowed entire decks to be shut down, or partially shut down using bulkheads instead of force fields to cut off those sections which would also save on power. This too would allow the phasers and shields to have more reserve power.
Cutting power to unused decks or, lowering output to some ships systems would allow the ships to keep phasers and shields at full output longer than what we saw the 1701D do.