Both are very useful... but they serve totally different functions...
For the purpose of removing parasites/Ick, I would suggest the UV light. The UV will "kill" the parasites while the diatom will only trap them. While both may serve your purpose I would tend to believe that "killing" them is the better approach...
I cleaned up your post a bit for clarification. If I changed your point at all please correct me...
But if the above is what you meant, it is not true. "UV lights" as used on aquariums or ponds emit UV-C radiation. Pond & aquarium UV's do so in the exact same way with the exact same effect. The single difference is the way they are suggested to be used.
Pond UV are recommended for higher flow rates at lower wattage, because this recommendation is only trying to offer a solution to green water (killing algae) and not killing parasites which requires a much lower flow rate at a much higher wattage.
UV-C is deadly to any/ever form of life. The more complex the organism the higher wattage and/or longer exposure it takes to kill it. parasites are more complex of an organism than algae, thus it takes higher wattages and/or longer exposure times to kill parasites in comparison to algae...