That Public is a good bike, a tank really.
I think the Giant has the better frame of the two.
Of course, there's a Via with an internal gear hub. It's only a 3-speed, which is good for flat to mildly rolling terrain.
The 8 speed IGH on the Public is a monster hub. You won't find those on many bikes in that price range.
The thing about internal gears is they are enclosed and very very low maintenance. But they are also less efficient than derailleur systems. You don't sound too worried about efficiency or speed. You'd probably be happiest with a bike you seldom had to service. So it would be hard to go wrong with an IGH for you.
The good thing about derailleur systems is that they're easy to service. Any decent bike shop can do it. And of course they are more gears per dollar.
It's kind of a tossup, and you won't go wrong with the Via in derailleur or IGH, or that Public. All very good if you want a laid back bike. I say get the 3-speed Via if your rides aren't real long or hilly. otherwise, very tough to call between the Giant and the Public. Guess you need to test them both.