The key problem in this kind of analysis is holding all of the possible variables equal while you change only one factor. Weight, construction materials, tread pattern and inflation pressure are all at least as important if not more important that tire width when it comes to rolling resistance. That said, VeloNews has an interesting article where they tested various tires at different pressures.
From Resistance is futile: How tire pressure and width affect rolling resistance
Tire rolling resistance on the road is caused by (1) internal friction and hysteresis (deformation over time) within the tire’s materials, and (2) on rough roads, small bumps lifting the bike and rider slightly (uphill) on each little impact.
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If a wider tire is made of the same materials in the same thickness as a narrower one, it will roll faster, because (1) the internal friction and hysteresis within the tire’s materials will be lower, and (2) because the surface imperfections in the road will be absorbed into the tire more easily (since it has more deflection available), thus lifting the bike and rider slightly less with each little impact.
The key in these tests was that they compared the tires at different widths but at the same pressure. What you are experiencing is likely that you are running the 28mm tires at a lower pressure than the 23mm ones. On a smooth road, minimizing the area of the contact patch becomes more important to rolling resistance, so the narrower tire at the high end of pressure will be fastest. That's why you will see velodrome riders using specialized tires that have a max psi of 185 or more.
On rough surfaces, however, a tire at lower pressure is able to absorb more of the bumps than a tire at higher pressure, with less deflection of the bike and its rider. This is the same “sprung vs. un-sprung weight” argument that demonstrates why suspension makes a bicycle faster on rough terrain — it takes less energy to keep the bike rolling if only a small amount of weight is lifted (like a small section of the tire) than if the entire bike and rider is lifted by the bump.
In addition, it's unlikely that your 28mm tires weigh the same as your 23mm tires, so the additional weight is going to increase your resistance. In all, it looks like if you are trying to minimize your rolling resistance on this smooth section of road, experiment with the narrower tires at different pressures. Just be aware that wind resistance is far more important at any significant speed. Wearing a slightly flappy shirt may make a bigger difference than the 5-10psi change, or the 5mm of extra rubber.
