Moving to 700x32 will be a little narrower, but it would be a good tire for a Hybrid. the number after the x is the width in millimeters.
What are your objectives for upgrading your tires? Speed? Comfort? Flat resistance?
I don't know the stock tires, but based on what I have seen/heard would guess that they are reasonable tires. The Gatorskin tires are well regarded for flat protection, while performing pretty well. I have had good experiences with Michelin tires I have ridden, but don't know that particular model.
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Slow Ride Cyclists of NEPA
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