In an attempt to put things to rest, I decided to do a little experiment to see if there was any truth to it at all. All tests were performed with the "gmahou" romset in Shmupmame 4.2 and frame-counting the resulting gameplay recording. In all cases, at least 3 tests were performed for each data-point listed, and all observations were consistent within 0-1 frames. (In other words, I'm pretty damn sure all of these numbers are reliable.)
First off, here are the claimed effects that you will gain if you complete each specific item set:
Since some of these are clearly harder to test than others, I decided to go for the easily-verifiable ones: the ones that can be easily measured visually, and for item sets that can be completed very early on. The most obvious candidates are shoes, food, and axes. I chose shoes to start with.
Shoes: movement speed up
I did measurements with a few different characters, both with no items at all, and with 8/8 shoes complete. The measurements below are how many frames it takes the character to move horizontally from one side of the screen to the other, with no obstacles.
Clearly, there's a difference here. Interestingly, it doesn't seem to actually be the same for all characters (Miyamoto has a smaller percentage increase than the others, probably because he's fast enough as it is).
Axes: charge shot duration increased
Next, I decided to try axes, since that seemed like a more subtle effect that would be interesting to measure. The measurements below are how many frames it takes for a full level-8 charge attack to complete from beginning to end (first visible frame of animation to the last pixel emptying from the charge meter).
Again, seems like there's truth to this. Once I confirmed that the axe effect was true too, I didn't bother to test other characters with it, because frankly, I was convinced at that point. I haven't tested the other (reasonably testable) sets yet, but hopefully this is enough to indicate that it's pretty likely that all of them are true.
One small thing that I noticed that might have led to past confusion is that these effects do not take effect immediately upon completion of the set; the buff will take effect at the start of the next stage or the next time the player dies, whichever comes first.
