The turn based system leads to a kind of problem-solving game, especially if you get to choose the order of playing your units.
Here I must disagree. Both approaches are about problem-solving. There is pause, it's not something like Running with Rifles, or Cannon Fodder at all, the time to think is one keypress away.
I think Jagged Alliance 2 has the best system for unit-level firefight : turn-based mostly, you decide what you want to do during interruptions (it's often more profitable to stay hidden), and the whole simulation is automatically real-time when the opposing sides can't see each other. The latter is invaluable to slowly creep toward an enemy position, or when combing the area for the last enemy.
While JA and JA2 are on par with UFO:EU in the pantheon of PC games, let's not forget that the all-out pause-mode simulation grew in part out of frustration with the lack of fine-grained control in JA realtime mode. Brigade E5 and later 7.62 were designed and written by a group of hardcore JA2 fans after all. Execution was abysmal, polygonal maps were crap, indestructible, small and full of bugs, and you could control every sneeze of your units and every cartridge in their magazines, which was at times a pain, but the idea was sound.
Still, JA/JA2 are loved at least as much for the detailed character design as for the tactical gameplay. Heh, I've ripped out the JA2 speech pack to serve as a alert/ringtone collection.