I'd pass on the QT. Technically not a moped, and legally can't be plated as one with the DMV.
the ad sounds sketchy, and they're ugly and slow as fuck.
The Puch sounds ok, but it always makes me laugh when they say "probably just needs the carb cleaned."
That usually means it doesn't run and they don't know why, or they do know, and it's much worse than a carb clean.
And considering it takes about 15 minutes to clean a tiny moped carb, anyone who doesn't do it so they can sell a running bike for more money is retarded.
But it looks pretty. Maybe you can sweet talk someone from here in your area to check it out with you before you buy it.