The main thing is how high the bars are relative to the saddle. Higher bars and longer top tube (= bigger frame, longer stem) let you get stretched out without putting so much weight on your hands and wrists. You'll wind up with the feeling of a more 'suspended' bike (at the price of catching a little more wind) and you'll also likely be able to climb a bit better.

What non 'race' frames might afford you is a 1) means of getting the bars higher (you want them high enough that you can ride in the drops just casually and not only reserve that for times you want to make a special point) and 2) clearance around the frame and fork for wider tires, like 28mm tires.

Wider tires = lower tire pressure = more forgiving ride, and if the weight bothers you just use extralite tubes. You can get these properties in some race frames but not all, so it's well to take a look. The bar height thing can be addressed in part with a stem.