Fatter tyres have lower rolling resistance at a given pressure, but matters are complicated by the need to use lower pressures to achieve equal comfort (because the casing tension is higher at the same pressure) or better.
There is also the problem that tyres of the same model but different widths do not always have identical casing and tread construction.
Rolling resistance is not the only thing slowing you down and it’s likely that the effect of aerodynamic drag is underplayed in the current industry-wide fixation on wider tyres.
As a general rule:
- the lighter you are,
- the faster you ride,
- the smoother your roads are,
- the less aerodynamic your rims are,
- and the faster your tyres are,
… the narrower will be your ideal tyre.
So for someone like me, who’s 65 kg and rides mostly on smooth tarmac, often in groups, with practically box-section rims and high-quality, supple tyres, I conclude that tyres over 25 mm are probably counterproductive.
Audax riders know more about long-distance riding than I do but I still think their tyre choices are often irrational. At slow speeds rolling resistance absorbs proportionally more of your power and on long rides the time gains from fast tyres are much larger than time lost to punctures. Besides, fast tyres are usually also more comfortable and that is its own gain.
The main thing is to use fast and comfortable tyres rather than tyres of some specific width, because the net effects of width are marginal among likely candidate widths.