Everything else equal is a fatter tire likely to get fewer flats
Actually misread another question
Is a bigger wheel likely to get fewer flats?
So I am posting this question to match my answer
Wouldn't a wider tire also hit more sharp objects because of the increased contact area? In that case it would be less likely for a narrower tire to puncture.
I say this from experience in the southwest where goat-heads(puncture-vine) are everywhere. I find that my roadbike tires get flats much less frequently than my mountain bike tires, but I also ride them in different areas.
The two most common types of flats are
Can also have the spoke puncture the tube from the inside but nothing a tire can do about that.
A fatter tire is more resistant to both pinch and puncture flats.
A larger tire will also have softer ride (due to lower pressure) and better traction due to more tire in contact with the road. This durability and comfort come at a cost. A larger tire is heavier, more wind resistance, and more rolling resistance.
Wheel sizes are reported in a number of ways.
For sake of fair comparison I will use actual wheel size.
Will compare ISO 622 wheel diameter and tire diameter of 1" versus 2".
The tire must support the weight of the rider and bike.
The 2" diameter tire will run at a lower pressure.
A bigger tire runs at lower pressure because it has more contact area.
Pinch flat is when the tube is pinched against rim and splits open.
A larger diameter tire is more resistant pinch flat for two reasons 1. With the larger diameter the outer tire (starts) further from the curb. 2. Due to the bigger diameter the fatter tire builds surface area faster so it does not need to deform as far to match the force of the curb.
A sharp object penetrates tire and tube.
Identical rubber will have the same force per surface area to penetrate.
Assume a triangular piece of glass 10mm by 10mm by 10mm.
Along comes this this fat soft tire. The tire deforms and the rubber makes contact with the road around the glass like the glass is not even there. Because the tire deformed and made contact with the ground the glass never exceeded the minimum force to penetrate the tire.
Even if the fatter tires comes in contact with more glass is still distributes the load.
Then along comes a hard shinny skinny tire that cannot absorb the glass and at the point it is just tire on glass there is sufficient pressure for the glass to penetrate the tire. The higher pressure tire did deform but not as much as much as the lower pressure tire. In this example when the tire was directly on the glass no tire was in contract with ground to take the part of the load.
A smaller piece of glass in which both tires deform and touch ground around the glass the softer (lower pressure) tire is always going to have more tire on ground around the glass and take more weight off the glass. The large tire is going to take enough weight off the glass to avoid penetration for a range of heights and sharpness.
This is not an artificial condition. A glass bottle is about 4 mm thick. The small sharp shards of glass from the bottle are 4 mm.
Even a piece of glass that penetrates both tires the glass will penetrate the harder (higher pressure) tire further. Because of deformation the glass will not be pushed in all the way. Again the softer tire has more deformation. So could have a case where the glass penetrates the tube on the hard tire but not the softer.
If you ride the same piece of glass long enough it will eventually works its way into both tires. So inspect your tires for glass. On a regular basis. For sure every time you air them.
Tire pressure effects both pinch and puncture flats (and rolling resistance).
Increase pressure reduces pinch flats.
Increased pressure increases puncture flats because the tires does not deform as much (spread the load).
So there is a sweet spot. Go with the manufacturer for that sweet spot. Tire will have a pressure range. If you weigh 180 of more then use the maximum. If you wight 140 of less then use the minimum. In between use liner interpolation. If you weigh 160 you are 1/2 between and should use the pressure 1/2 way between.
Mountain bikers like to run at lower pressure for more contact (traction) and to absorb roots and rocks. If you are running at a lower pressure then be aware and don't bang on roots and rocks as hard.
Tubeless tires offer the advantage of no tube to pinch so no pinch flats. Can run them at a lower pressure. A tubeless tires with sealant is not less susceptible to a puncture flat but it will seal small punctures.