I love the 300 WSM. My best 1K BR rifle was in 300 WSM and it dominated the competition. I currently have a 7.75 lb w/scope M-70 Classic/Benchmark/Edge in 300 WSM that is amazingly accurate.
However, there is no way a 300 WSM can shoot as fast as a 300 Winny. It is all about case capacity, and the shape between these two cases doesn't have a huge effect on velocity. Further, comparing the numbers we get with our handloads in a couple of rifles really doesn't tell us much other than what we can get those rifles to do.
The biggest question mark when we work up handloads is knowing pressure. I have personal knowledge of no less than five guys who have used Oehler 43s to test pressure. One of these fellows was an ballistics consultant for the US Army. They all agreed there really isn't a reliable way to tell when we are at maximum pressures. All of the conventional pressure signs: flattened primer, sticky bolt lift, case head expansion, etc; only tell us when we are well over maximum pressures. One particular lot of Remington brass tested to 80,000 PSI without showing and signs of pressure.
That leaves us with the data the bullet and powder makers publish as our best reference for velocities obtainable for a given bullet/power/barrel length combination. This data has been scientifically obtained using high-end pressure equipment, and enough shots are fired to get statistically meaningful data.
The 5th edition Sierra manual shows a 300 WSM with 190 and 200 grain bullets at 2900 FPS from a 24" barrel. It shows the 300 Winny shooting the same bullets at 3000 fps from a 26" barrel. We can add 50 fps to the shorter barrel, but the WSM is still falling short of the Winny. They don't show any data for a 240 grainer in the WSM, but they do show the 300 Winny getting 2800 FPS with a 240 grainer in a long throated rifle. There are many reasons why your own 300 Winny may have shot so slow, but it wasn't the norm.
A general rule of thumb is to take the 1/4 of the difference in case capacity to get the increase in velocity. A 300 WSM holds 80 grains of water, a 300 Winny holds 90 grains of water. That is a 11% increase, and 1/4 of that is 2.78% At a MV of 3000 fps, 2.8% equals 84 fps. Now the 300 WSM will effectively have 1/2" more barrel length than a 300 Winny in the same length barrel, and that is worth nominally 25 fps. We are again at a 50 fps advantage to the 300 Winny.
That is a 50 fps gain for the Winny in the Sierra manual, a 50 fps gain in standard calculations, and even a 50 fps gain with 240 grain SMKs in long throated rifles.
Now without question we get more velocity per grain of powder with the WSM over the Winny, but that is true almost every time we downsize case capacities, and the converse is true when we add case capacity. Regardless, when a 300 WSM and a 300 Winny are both throated relatively the same, shot in the same length barrels with ammo loaded to the same pressures, the 300 Winny will be a little faster.