The Soyuz Class Starship is a modification of the Miranda Class (this fact is in contention - see below). Incorporating weapon design advances initially developed for the Constellation Class exploratory cruiser, the Soyuz Class refit was a way of keeping the older Miranda Class spaceframes in service while negating (or at least redistributing) their tactical shortcomings. The Miranda Class was a heavy frigate; Soyuz is classified as a tactical cruiser (remember, this is back before Starfleet got all touchy-feely about their spacecraft being construed as warships. Soyuz is a warship, plain and simple).
Changes to the Miranda Class Spaceframe
Miranda's rollbar has been removed, replaced by two massive phaser cannon (one dorsal, one ventral). These cannon are fixed to the hull atop an extended aft engineering section that incorporates a larger warp reactor and a third shuttlebay installed between the previous two. With this added bay, Soyuz Class starships are capable of launching and supporting three independent squadrons of attack fighters or ground forces and transports.
As if that wasn't enough, two additional phaser cannon were mounted on the port and starboard surfaces of the primary hull directly above the warp nacelle pylons.
Soyuz Class starships were supposedly designed to bear the brunt of a full frontal attack. This retrofit sacrifices the aft phaser arcs of the Miranda Class while significantly improving its forward attack power - they were tasked with getting in, doing massive amounts of damage (or deploying fighters and/or ground troops) and getting out again. They're tanks.
What doesn't make any sense is that, keeping their mission profile in mind, why the refit didn't include a real deflector dish (or, barring the possibilities of that, why they didn't retrofit a different existing spaceframe). One has to assume that the damage the class can take in combat is minimal.
Continuity Issues
Some say Miranda was a Soyuz Class variant rather than the other way around. This may be true as far as the timeline is concerned, but no canonized sources exist to back that claim up. Then there's the fact that, as far as the model builders are concerned, all of the Miranda spaceframe variants are redesigns of the USS Reliant model from Star Trek II: The Wrath of Khan. Without source material saying otherwise I'm going to assume that the order in which the models were designed and built in the model shop is parallel to the way they were built in spacedock.