I've ridden 23mm tires for the past five years, but have decided to go with 25mm tires on my new bike.
First of all, I've noticed that not all manufacturers use the same measuring standards.
For example, my 23mm Schwalbe Ultremo's look as large or larger than Continental's 25mm offerings.
So, the 23mm tires from one manufacturer and the 25mm tires of another manufacturer might overlap or coincide in size, or even seem marked in reverse, with the larger tire marked smaller and the smaller tire marked larger.
I have in the past ridden 23mm tires because of their low weight.
I find that low rotating inertia makes for easier acceleration and braking (I don't skid).
The newest offerings in 25mm come so close to the weight of 23mm tires in the past, that I see no penalty in riding a 25mm tire.
As for advantages in riding a 25mm tire, I think the slightly lower tire pressure will mean a slightly lower percentage of flats.
Given my very heavy body weight (220lb - 235lb), I think the 25mm tires will treat my bike frame a little more kindly, since my bike frame has to absorb both my weight and the road vibrations.
And, finally, I've read several papers now that suggest that on the street, meaning, not on a smooth track but on an irregular surface, the 25mm tires with their slightly lower pressure actually have a lower rolling resistance when one takes surface irregularities into account.