Hi,
You should get tires that are designed for where you ride. If you are riding on paved trails, then 28mm road tires are going to be fine (and a
huge improvement over knobby tires which are silly for the riding most of us do).
If you are riding on crushed limestone, I'd recommend a wider tire (35mm up to 42mm). I've ridden 28mm tires on crushed limestone and really didn't enjoy it.
As pointed out earlier, being upright on a hybrid bike is less aerodynamic than being in the drops. That being said, if you aren't comfortable being in a road bike position (and I'm not), then stick with the bike on which you are comfortable.
And as been pointed out, the most important thing: If you want to ride faster, ride.
Cheers,
Charles
p.s. For your original question, yes, please, change your tires.
