Be sure the new tires will fit the fenders (assuming your Public bike has them -- most I've seen do). Brakes too. Tires vary quite a bit from nominal specs. If your bike has fenders go for the 32 wide Armadillos just to be safe.

I have a set of Specialized Hemisphere 700x38 that seem pretty close to 38. And an Innova 700x38 that's a bit narrower, an Innova 700x35 that's closer to 32. A pair of Continental 700x42 that are actually closer to 38 wide. A pair of Michelin 700x40 that are closer to 45 wide and quite a bit taller than anything else I have. The 700x42 Contis and 700x40 Michelins aren't at all similar -- at a glance anyone would pick the Michelins as being the larger in nominal specs, but nope.

In actual ride characteristics, the width isn't the major factor. The tread design and inflation matter more. I can run the Michelins and Contis at low pressure safely where they're much more comfortable at no cost in perceptible rolling feel. Where I really feel a difference is on patches of sand, pea gravel or large sharp railroad ballast gravel. That's where the wider Michelins feel more secure at lower pressure (around 50 psi, much lower than Michelin's recommended 75-85 psi). Otherwise, I can't say I feel much difference between the 700x35 and 700x40 or 42 tires.