efinch, I consider this question on a par with "do you want bubonic plague or smallpox?" or perhaps "would you prefer hanging or lethal injection?"
frogbit I know nothing about, but duckweed....is OF THE DEVIL! Ugh, ick, spit, ptooey. And ack and hack as well. Bah humbug. Vile and evil stuff. Nasty. High on my list of things I would not miss if it vanished from the planet tomorrow. Wouldn't wish on my worst enemy. Given a choice between it and hemorrhoids I would stock up on Preparation H.
not that I have strong feelings on the subject or anything.

And it IS possible to eradicate a duckweed infestation, it just takes six months or so of fanatical daily diligence to locate and pluck out every single tiny leaf. A three-finger grab is the best technique, keeps it from scooting away (most of the time) due to surface tension. Remove every existing particle. Feel triumph. Repeat the next day. and the next.....and the next....you get the picture.
shun the duckweed. Chances are you will be afflicted eventually by accident, as noted above. But you never want to look at it and know you did this to yourself.