Mr. Christie’s town-hall-style meetings here are stripped-down, unfussy affairs, so determinedly casual that his staff picks coffeehouses, bowling alleys and even bars as sites. (Bars are inexpensive, staff members say, and the setting all but guarantees a crowd.) He uses no stage or barriers, just a microphone and a bottle of water with the label ripped off. He plops himself down in the middle of the room and wanders into the crowd and plays for laughs at almost every turn: The audience at a cafe here broke into laughter 21 times.

Mr. Rubio’s events are much more meticulously planned, so formal that cloth-covered fencing is set up around the perimeter of the room. (Aides said it made the young lawmaker seem more presidential.) He speaks the entire time atop a raised platform, flanked by enormous red-white-and-blue campaign posters lit by spotlights. Polished applause lines tumble from his mouth: In Clinton, Iowa, the crowd interrupted him at least 15 times with bursts of clapping…

Mr. Rubio favors lofty, patriotic, high-minded narration to make his points; Mr. Christie relies on emotional, sometimes borscht-belt-style storytelling that can drag his events to two hours, twice as long as Mr. Rubio’s…

Mr. Rubio’s style can be stirring — or oddly disconnected. When a young woman at his event in Clinton wondered what he would do to lure millennial voters to the Republican Party, pointing out that she was one of just a handful from that generation who came out to see him, Mr. Rubio delivered a rehearsed-sounding answer heavy on campaign talking points instead of an actual strategy. “Here is how we are going to fix it,” he said. “By allowing free enterprise and limited government to be applied to the challenges of the 21st century.”

The young woman looked unpersuaded.