Well, as the premier Heavy Cruiser of the fleet, one of the largest ships in the fleet, and a brand-new, bleeding edge state-of-the-art starship, the Sovereign WOULD be a prestigious command. She wouldn't be the everything-and-a-dozen-kitchen-sinks capital ship that the Galaxy is, but she would be doing much more day-to-day operational work. The Galaxy would be used when there was a need for a stand-off, or when the Federation wanted to be extremely impressive. The Sovereign, however, would be the iconic face of the Federation.
Think on how the Excelsior was used in the first half of the 24th Century. No longer Starfleet's premier capital ship, the Excelsior still served with distinction as Starfleet's premier and workhorse Heavy Cruiser. They built a crap ton of them, and they were everywhere, doing everything both locally and in deep space. After the 2350s, when their age really started catching up with them and Starfleet started fielding newer cruisers, they got bumped down to a lot of the muckity-muck crap assignments that the newer, more capable cruisers would have been wasted on, but before that, they would have been the representative of Starfleet, the ship that got out there, and got its hands dirty, but still carried the image of the Federation.
The Sovereign is taking over that lineage. In a lot of ways, it's what the original Constitution class was (and the naming of a Sovereign class USS Enterprise is a return to that role), and like the original Connie and the Excelsior, the Sovereign is going to be the face of Starfleet and the Federation going into the 25th Century. It's not prestigious like the Galaxy class is, but it's not less prestigious (though the Galaxy class gains prestige points from rarity that the Sovereign, which will probably be produced in relatively high numbers, won't get). The Sovereign has a different kind of prestige than the Galaxy class, or perhaps it would be better to say that it is prestigious for different reasons. The Galaxy is the biggest and most powerful ship in the fleet, the no-holds-barred, everything-and-a-dozen-kitchen-sinks class. It's the awesomely powerful ship that represents the pinnacle of what the Federation and Starfleet can achieve. The Sovereign class isn't that, but it's prestigious because it represents the core of what the Federation is on a day-to-day basis, and really represents the heart of the Federation: It's sleek, fast, very advanced and powerful for its size, and while it only has five kitchen sinks instead of a dozen, it's not going to be reserved for special cases. It's comfortable, presentable, more than capable on all fronts, and it's going to be there even when it's not a special occasion, unlike the Galaxy which is going to largely be reserved for special, higher-profile duties, because they're so resource-intensive and relatively few in number.