While we never saw direct on-screen evidence ... indeed, the designers of Voyager stated that it's essentially a downsized Galaxy class with same shields and weapons in terms of power outputs.
The only major difference between the two would be the obvious: size (along with amount of crews and torpeodes/materials both can carry in stock ... not to mention a temporary superiority in computers going to the Intrepid because it came designed with bio-neural circuitry ... and it's definitely possible the Galaxies received them in one of their re-fits later on).
It makes sense that SF would be able to make downsized versions of larger ships with same capabilities (whereas smaller ships would be limited in terms of how much torpedoes/materials they can have in stock).
They are easier/faster to produce, and they'd likely have very limited supply of civilians/families on board (if any at all) when it comes to deep-space exploratory missions.
If SF for example wants to reduce the amount of spent resources when it comes to making new ships ... instead of making 2 Galaxy class ships ... why not make 1 Galaxy class and 2 Intrepid class ships?
You get 3 ships instead of two, and granted you are limited in the amount of civilians/families you can stuff on the smaller ships ... still, it's a better arrangement because you'd have new ships out in the field much faster, while getting the same job done.