In the movie, Nero is 154 years ahead of the time, and allegedly uses Borg technology - a threat unknown to the Federation at the time. How is it possible that Nero doesn't simply destroy the Enterprise? The technology is way beyond the Enterprise.
Nero initially doesn't want to destroy the Enterprise. He wants Spock to suffer first, which is why he deliberately inflicted less than fatal damage during his surprise volley.
His ship may be from more than a hundred years in the future and enhanced with Borg tech, but it's still a high-tech Borg-enhanced mining barge. He managed to annihilate the main fleet because he attacked from ambush, but in a straight up fight if they'd seen him coming he wouldn't have managed, in no small part because...
Frankly, just going by his observed behavior in the movie Nero is a fricking moron in terms of strategy, tactics, or ship command in general. It's understandable why his government didn't deem fit to trust him with anything more powerful than a mining barge.
It's just a mining ship, that's why.
It has an advanced payload (apparently at least 25 years worth of guided missiles - so, like, 38) but its primary function is that of a simple mining ship. Enhance it all you like, but without a Constitution-refit style teardown/buildup again, it's still a workhorse, not a war machine. To invoke parable -- one could weld a chain gun to a 21st century bulldozer, but that doesn't mean one could travel back in time with it to change the entire outcome of the Civil War (at least not without better strategic planning than Nero executed).
As for the handwaving of Borg enhancements to explain the Narada's apparent superiority -- eeeehhhh. The stuff about Borg tech/Tal Shiar/etc is from the comic, and its legitimacy as canon is… iffy? I'm aware of the interview were someone (Orci?) stated it is, but that would be yet another anomaly in the concert of oddities that permit new Star Trek's unique rules about space, time, Federation guidelines for bridge lightning, and now apparently offscreen works to be permitted as 'canon'. Roddenberry was more or less the godfather of the retcon, but even where published works are considered to have certain grey areas, comics have a pretty hard and fast rule about being "right out", as it were. http://en.wikipedia.org/wiki/Star_Trek_canon#Other_publications
Besides, since when did "Borg enhanced technology" include guided projectile weapons? The Borg's primary weapons are beam and energy weapons. Adaptive shielding, focused lasers and that. The Narada doesn't spend much (if any?) screen-time tearing into starships with its planet mining laser drill, so one can only really prove it relies on those fleet-seeking missile thingies (unless that's in the comic too, but I'll point to my previous statement on comics as canon).
Nero does attempt to at first during the surprise attack. He hits the ship hard and would have destroyed it if he hand't seen that it was the Enterprise out of all ships.
From the comics we knew he read the historical data of the federation and thus also knew that Spock served upon that ship and for Nero all revenge is best served cold.
Thus destroying the Enterprise would kill Spock way too early even if its only the young Spock. He wanted him to suffer thus he stopped the other barrages that would have destroyed the ship from being fired.
Else the second wave of Torpedoes would have done the Enterprise in (what is more surprising is that the Enterprise took less of a beating than the Kelvin and was in a way worse shape according to their own crew..."another hit like that and we are done for"!).
The 2009 reboot ends Star Trek having basis in science or logic. It's now an action film more on the lines of Star Wars. (This is not of itself a bad thing). Hence the Enterprise surviving is required for the action and plot.
For example, once the enemy ship is bisected by a blackhole you no longer need to open fire with all weapons ..
Research used: http://redlettermedia.com/plinkett/star-trek/star-trek-09/ (Red Letter Media Review)
From a purely practical standpoint, if Nero destroys the Enterprise in the first encounter, the movie is over--and so are any possible sequels.