One point for people who are not aware of it and that I usually get harassed for reporting, is the propulsion problems from time to time on the Millennium, Infinity and Summit. The last propulsion failure for the Millennium was on a cruise from Australia in March of this year, which resulted in the usual missed ports and the next cruise being cancelled on very short notice. That said, for a cruise to the Caribbean where for me getting to all the ports are not that important anyway it might be worth taking this additional risk.
While both cruise line will have their die hard supporters, either ship will offer good food, entertainment and service. So as far as that is concerned there is really no difference at all.
For a cruise that involved long travel to get to the ship or an itinerary that I really wanted to see, then I would go for the HAL ship hands down.