Let’s clear up a couple of things first. Tire grip or adhesion is independent of tire width, or ‘contact patch’. This is a common misconception, but if you look at the formula for computing friction between two surfaces, the variables are normal force and coefficient of friction. Surface area is NOT in the formula.
That causes some grief, and has cost Joe Racer a LOT of wasted money. There was even an F1 race team that was convinced they could get a cornering advantage by building a race car that had FOUR front wheels rather than two. The result: their car kept sliding out in turns, handling worse than their competitors.
In the sport of drag racing, engines have gone from about 2000 HP to 8000 HP (!) or more. They still use two rear tires of roughly the same size and shape as they always have, or roughly the same ‘contact patch’, even though power has gone up by a factor of FOUR. Of course tire compounds have no doubt improved, but the tire width hasn’t changed much. Again, there was a racing team that thought they could get better traction with four rear tires on a drag racer, but they didn’t find any traction improvement. (This is NOT to be confused with four-wheel drive, where all of a car’s weight bears down on traction wheels, vs just one end or the other of the car’s weight. In physics terms, this doubles the normal force, doubling traction).
It’s the same with braking. To get greater stopping force (with a given tire), you either press harder on the pedal, or you put on brake pads with a higher friction coefficient. To get greater braking capacity, on the other hand, you must increase cooling capacity (greater surface area), and mass of the braking components (greater short-term heat absorption capability). And for a given stopping load, larger pads spread the wear out over a greater amount of material.
The advantages of having more surface area in a tire anvelope are that you improve cooling, and for a given coefficient of friction, the tire should last longer because the wear is spread over more tread (this also is the case for a larger diameter). In the extreme case, like drag racing, a wider tire means a greater resistance to the tread simply shearing off (provided the material is tough enough).
Within the broader topic of handling, there are many considerations, such as sidewall stiffness/flex, tread pattern, suspension components, ride height, weight and weight distribution, front or rear wheel drive (or both), aerodynamic forces, engine power characteristics, etc. And wet surfaces cause havoc, especially with wider tires, when width can actually decrease traction because of the hydroplaning phenomenon.
After more than 50 years working in the automotive field as engineer, owner of tire and repair dealerships and having sold millions of tires in multi-state, multi-store tire/repair chains I would summarize as follows. As a rule of thumb, wider tires compared to original sizes will make the vehicle handle better. One of the reasons that German cars handled better was they used 2 to 3 sizes wider and one to two sizes lower profile than their American counter parts on similar class of vehicles. If you track road test on vehicles on the 300 feet diameter skidpad G forces, you will find most O/E tire sizes will not generate more than .86G while tire sizes such as low profile 30 to 40 series with cross section width from P245 to P325 and larger will generate more than 1.11 g. The suspension and weight distribution have a lot to do with it but generally on similarly equipped vehicles, the wider tire will generate better cornering figures and lower slalom times. The larger rim size also promote larger brake rotors so braking have improved as well. It is not unusual to see 13″ rotors where few years back the same vehicles only equipped with 11″ to 12″ rotor.
Tire width must be mated with wider rim for better handling and wear. Handling also depend on the aspect ratio of the tire and the rubber compound. An example of it is any high performance tire – Michelin Pilot Sport 4 will beat the same size tire with the same speed rating that is rated all season or has M+S designation. Lower profile means less sidewall distortion on turns and higher inflation pressure so efficiency will not suffer. Usually when the tires are of good quality and wider mounted to an appropriate rim for the road condition, they will handle better. Most of my comments are for day time driving on dry pavement. Wider tires can lower your traction and direction stability in rainy weather as hydroplaning is a major problem. Since passenger tire treads are only 11/32″ deep, water dissipation will always a problem. So if you encountering rainy weather, use caution and slow down.
Off-road and 4X4 may be different because the aspect ratio – sidewall is much higher for the purpose of “envelope capacity” the ability to roll over “envelope obstacles” rocks rather than bouncing over them, tire mass is much greater and concentrated on the thread area and rims are off-set to gain track width, they can be very difficult to balance and their radial force variation is much greater compared to low profile sizes, so harshness, vibration and noise will always be a problem. Furthermore there are all seasons, mud and all terrain type of tread designs optimized for road surfaces encountered. Inflation must be changed to fit the terrain and driving condition encountered as well.
There are a lot of engineering that determine what is the best tire size for the vehicle. On top of that the manufacturer also have to balance the price for the performance so they will be profitable. The consumer may have different uses of that vehicle and a specific budget for the modification. Get some professional input if you have special tire needs and you may be well rewarded.