Republicans set a new turnout record Tuesday in New Hampshire’s primary, attracting more than a quarter of a million voters to the polls and offering evidence that most of the energy in the 2016 presidential race continues to be on the GOP side. Democrats saw a strong turnout, but their two-person race couldn’t recapture the magic of the 2008 battle between Hillary Clinton and then-candidate Barack Obama — a race that presaged Mr. Obama’s eventual cruise to victory in November.