Is there a significant difference between the two types of protagonists?
Yes. In fact, I would go so far as to say, they are nothing alike. A cautious MC won't take chances. A Pragmatic MC will do the practical choice.
For example, Lets say I am bad at leading an army, but I hve an army I have to lead. My enemy is very talented.
The Cautious Choice would be to turtle up and build defenses.
The Pragmatic Choice is to bum rush ASAP.
The cautious choice will buy you time, but ultimately if they are better than you, you will lose.
The only PRACTICAL choice is to bet everything on a long shot. When the odds are stacked against you, but you MUST gamble, bet everything on one roll and let the die fly. Ergo, the practical choice is to mount up everything you can and just charge the mutherfucker at night. Yes, night attacks are bad, but they are bad for EVERYONE. I can't win with skill, but I might win with luck.
But If I AM more skilled, then I should turtle up and take my time, because time is on my side. Being Cautious is the PRAGMATIC choice.
Frankly, I don't even understand how you can make them 'vs'.