> Which one is the most popular/available style?
Personally I prefer the 2x7 row for ease of connection with ribbon cable and IDC connectors.
Though I admit the 14-way IDC cable/connectors are less common than the
10/20/26/40/52 way parts.
The single-row LCD version might be better for soldering in a row of pins to plug into those plastic breadboard things.
If I were an equipment maker, and wanted to mount the LCD on a front panel away from the PCB, the 2x7 seems best.