The answer is: It’s complicated.
Wood screws or any type have very high tensile (pull-out) strength. Try using a claw hammer to claw out a nail, and it will generally pull out easily. But try that with a wood screw and good luck to you.
But wood screws fare poorly in shear strength. Construction bracket manufacturers have long insisted on nails for their installation and not screws for a good reason. The fixed hole size in the brackets limit the size of the fastener. As I recall Simpson Strong Tie brackets call for 10d nails (0.162” diameter). A wood screw with a similar outside diameter will probably have a core diameter (which relates to shear strength) of about 0.145” - 0.150”.
In addition, the screws get work-hardened during manufacture. If you have ever taken a wire clothes hanger from the dry cleaners and bent it back and forth several times to break the wires you will understand that a work-hardened piece of wire becomes brittle.
All threaded screws become work-hardened to some extent. The pressure of the rollers to roll in the threads does that. With machine screws that is good. Only the threads become hard and hard threads are good for durability.
But with wood screws, they are not only rolling in the threads, they are rolling in a taper. So the threads become hard (a good thing) but the core diameter of the wire also becomes hard and brittle (a bad thing—especially in shear strength).
To make matters worse, screws are often zinc plated. The plating process creates a situation called “hydrogen embrittlement”. If you’ve ever assembled something made in China and the screw head snapped off while screwing it together, then you are aware of hydrogen embrittlement.
Hydrogen embrittlement can be remedied by baking the screws at 300 degrees for a half an hour, but that must be done within 30 minutes of the end of the plating process. Failure to do so will make the product very brittle.
A few years ago, Simpson (“Strong Tie”) came out with special screws for use with their brackets. This was not done to save money. They are much more expensive than nails. And it was not done for strength. It was done because there are situations where swinging a hammer is difficult (though a palm nailer generally works well). It also makes disassembly easier (not usually a factor).
For use with construction brackets only use screws certified for that application. Using Spax or other construction screws would be a serious error.
But if you need pull out strength, then screws are superior.
If you have ever witnessed the rehabilitation of an older steel bridge, you will notice that they are removing the old rivets and replacing them with high strength bolts and nuts.
It would appear that the rivets would have the advantage as there are almost always assembled with the fasteners in shear. The rivets’ outside diameters are going to be larger than the core diameter of a bolt (the threads do not impact the shear strength.
But the rivets are simply peened over. The bolts get torqued tight. When they tighten the bolts it creates friction between the plate and the girder. That friction creates more strength than the shear strength of the bolts.
So, if the structure you are building can benefit from the friction between the two pieces of wood, through bolts will work better. But they may require periodic tightening as the wood shrinks with age.
Sorry to burden you with all this information. It is complicated.
But always use screws that are certified for use with the construction brackets. Or the nails that are specified. Do not substitute construction screws for that application.