The NCC-1701. The one from from the 2009 film.
And the movie stayed true to a Star Trek tradition of not keeping shields up at high warp: in ST6:TUC, Sulu does the same when fully well knowing he is going to enter a battle zone.
Indeed, I'm hard pressed to find any examples of our skippers maintaining shields during warp even in wartime, as long as they feel confident there are no threat forces in the immediate vicinity!
They only sacrificed any of the three because of treaties and technological limitations, heavy cruisers were bound to a 10.000 ton displacement figure which set limits to what you can do, battleships were limited at 35.000 tons, if there hadn't been any treaties the brits would have ships already in the late 20's/early 30's which were pretty damn close to the Yamato class in terms of firepower and protection and battlecruisers which were pretty damn close to an Iowa but with heavier armour, what was left after signing Washington naval treaty became the Nelson class which sacrificed speed primarily.Well in the real world, warships of various designs have to balance speed, fire power and protection. I may be oversimplifying here but, as an example a heavily armed, heavily armoured battleship must sacrifice some of its speed. Battle Cruisers sacrifice armour protection for speed and fire power, whereas heavy cruisers generally sacrifice armour and fire power for speed.
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