For pre 2017 engines it does not matter but for newer gas engines it is foolish not to use the new motor oils that the engine manufacturers worked with the oil companies to develop over a period of years. To get an idea as to what is evaluated by running engines and then tearing them apart:
New motor oils that meet the API SP and API SN and SN Plus (cans have a Starburst symbol), the lab motor oil tests are worthless.
These new motor oils are much more effective at low viscosity and need to be with their 5W and 0W ratings. The oils have to meet much more stringent testing that is based on actual hours of engine operation where the engines are torn down and the parts are examined and the wear is measured.
The new test requirements cover kinematic viscosity increase at 40 degrees celsius, piston deposits, average cam plus lifter wear, cam wear, engine sludge, rocker cover sludge, engine varnish, oil screen sludge, hot stuck rings, cold stuck rings, oil ring clogging, bearing weight loss, aged oil low temp viscosity, phosphorous retention, high temp high shear viscosity (this is critical with multi-grade motor oils to avoid polymer shearing), evaporation loss at 250 degrees celsius, percent flow reduction with various level of water in the oil, foaming tendency and stability, high temperature foaming tendency and stability, homogeneity and miscibility, high temperature deposits, emulsion retention, and elastomer compatibility. None of this information can be provided by consumer oil analysis lab.
If an oil meets these specifications then it will do the job. For my 2018 SUV I use Mobile 1 simply because it is easy to find. Amsoil is not fit for my diesel truck with its poor additive mix and not reason to pay more for less. For the diesel truck I use Valvoline Premium Blue which also happens to be what Cummins uses. The Valvoline has one of the best additive mixes for diesel engine use and it is reasonably priced and it is also available at the local Ram dealer.
A heavier weight oil is going to provide less protection when the engine is cold and that is when most wear tends to occur. Use the weight that the engine manufacturer recommends as their engineers know what will maximize the life of the engine. Pretty dumb to go by ads in magazine or a seat of the pants gut feelings when trying to get as many hours of use as possible.