The thing was ugly and scary looking, but like it was stated before it's a working ship, it's not made to be pretty. Of course it would have no problem taking out a ship from the 23rd century. In "In a Mirror Darkly" from ENT they get their hands on a Constitution class starship named the Defiant and it has no trouble running right through anything thrown at it in the 22nd century.
Different situation entirely. In its day, the Constitution class was the most advanced ship in the Federation. Throw one of those back 100 years and have it fight contemporary starships from races that eventually formed the Federation, obviously it's going to kick their ass. It's like sticking a modern day fighter jet in World War I.
Narada on the other hand, as a "simple mining vessel" shouldn't really have been able to rip apart Starfleet's finest unless it had been upgraded. Stick a modern day oil rig in World War I. You're still not going to win any battles.
Also I don't think Nero upgraded Narada, he didn't have time. Spock was still running from the supernova, and Nero said that he had watched Romulus destroyed. It seamed to me that the nova, the destruction of Romulus and the getting sucked into black hole all happened in rapid succession with little time in between for doing repair/retrofit job's on a ship.
This is where the Countdown comic actually makes sense. Or as much sense as this storyline can make. It wasn't until after the supernova destroyed Romulus that Spock took off, and therefore, in Nero spent the interim time upgrading Narada. Just because the movie depicts everything in the span of a few minutes doesn't negate the possibility that it could have been over a prolonged amount of time.