And in STiD, they wanted the Vengeance to be outright superior to anything the Federation had at the time, so much so it would put NuKirk into a situation where he felt powerless, one of the main themes of STiD is that Kirk wasnt ready for the chair, the Vengeance is another story device to demonstrate that.
The JJ era ships clearly look superior to the TOS counterparts, then throw in Khan's contributions, his intelligence levels and ability to learn and solve problems beyond a normal intelligent human could, then backed by a mandate to build a no compromise battle ship, there is a convincing case for the Vengeance to be that advanced and combat effective in 2259.
"At the time" would sum up rather well how it would compare against the E-E. As for how well it stacks up against other Federation ships, the Enterprise is supposed to be the high bar by implication of being the "newest flagship" so... take that as you will. The JJ era ships are certainly all bigger than their counterparts.... but that doesn't mean better necessarily.
I do think you're wrong about the Khan being so super smart that he contributed to it. Take say.... Napoleon and move him ahead to World War 2 and drop him there... he's not going to be that successful... there were SO many new military concepts by that time, air power, armor, logistics were not only completely different but played a different role, military doctrine had changed. Everything he was a genius at would've been outdated. Not to mention that being an effective political/military leader as Khan seemed to have been.... has absolutely nothing to do with military design past or future. Bringing in Bonaparte to design a new tank in that scenario I laid out would be silly at best no matter how smart he is.