Lowering the nacelles gave better arcs to the P/S saucer phasers.
Lowering the nacelles also allowed for better space management in the secondary hull (more stuff) since things were, overall, lower.
Not so much different, as is a new class, and new ship, not a Star Fleet kitbash.
Belknap is larger, thus more overall room for stuff.
Connie is smaller, so less room for "up-gunning".
Connie with different internals in SFB/C: F-CA, CC, CVA, CVS, GSC, and all refits non-X. (may have missed a few)
Belknap with different internals in SFB/C: F-BCG, BCV (and variants), BCF, BCJ. Note, here the Belky represents the class as a whole, while the game spreads the BC over different classes.
Czar "Knowledge is power, and is half the battle," Mohab
P.S. and now you know!