Which eye antibiotic drop is better? I know each one has it's own class, but generally which is stronger polymyxin & Trimethoprim or Cipro (ciprofloxacin)?

All depends which. bug or bacteria you are trying to kill. That is the more important question. Otherwise you are building resistance to SUPER BUGS, and when you need to use a 'strong' antibiotic, it just won't work anymore. In that case, it becomes a weak antibiotic. Ask your doctor what you are treating to find out the bacteria in question. Then, answer it that way! Hope this helps!