First off, yes brass is an alloy, so this title is technically inaccurate. But that's the way the world refers to these things, so that's what we're using here.
One way to make a set of wheels as light as possible is to use aluminum (or aluminium, if we want to be really correct) alloy nipples versus brass nipples. As the pics below show, there is a roughly 30g difference between 44 alloy nipples and 44 brass nipples. To some that is insignificant, to some that is a modern tragedy, to some it is 31g. There is no doubt that many wheel purchases have been made on one set being 30g lighter (or at least being claimed to be so) than another.
If you asked people "all else being equal, would you like your wheels to be 30g lighter," almost all of them would say "yes please."
There is enough uncertainty over what exact impact (or even to within an order of magnitude what impact) weight plays in cycling. Rotating weight, like the role that nipples play, is even more clouded. Some whip out a physics calculation that shows the simple standard inclined plane model and claim X, others will apply more complicated means and tell you that it's much (much) bigger than X.
I honestly don't know what to think about that end of it. I'd be one of the "almost all" people who would choose 30g lighter, all else being equal. Simply, I don't believe that weight is inconsequential, but neither do I think that 30g in a set of wheels, even if it's at the rims, is an absolutely decisive change. Enough for me on my best day to beat me on my best day with all else being equal except for changing out alloy for brass nipples on a favorite climb, like Appalachian Gap in Vermont? It's probably worth a couple of seconds there, sure.
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I also know that, in my experience of riding, I believe that I've sensed/observed a bigger performance difference in light versus heavy wheels in what I'd call "low inertia" riding situations. Ripping through a flat four corner crit, I don't think wheel weight plays really any significant role at all. On a cross course, where you're accelerating hard from nearly a dead stop every 12 seconds or so, weight seems a bit more important. Switching from a 780g tubeless ready mountain bike tire to its otherwise closely equivalent non-tubeless 600g cousin seems to make a big difference. There are also some construction differences there which would favor the light tires, and I obviously couldn't parse those out. These experiences and biases flavored our decision to do carbon cross, gravel and mountain bike builds - in addition to the absolute requirement that they be good and quality products, we needed to believe that there was some there there in terms of performance benefit, and that is the case (there is also some longevity benefit there as well).
So that's as much as I can tell you about the weight piece, but what about the "all else being equal" piece?
Brass nipples are stronger. Some nipple manufacturers will tell you otherwise, and they'll have data to back it up. The problem with that data is that it measures brand new nipples in a lab environment. As much as I love Raoul Luescher's videos, when he showed a test of alloy versus brass nipples (buried in another video so I can't search for it), he just screwed some nipples onto spokes and subjected them to corrosive conditions, which is exactly what we did a bunch of years ago (sometime in 2014, but I can't find it to link to it). The problem with that is that the spoke isn't being abraded against the rim in build, and there's no dynamism in the thing. He didn't find corrosion in his test, we didn't in ours, but you do see corrosion in alloy nipples in wheels. And corrosion compromises strength. We prep the rims to prevent a sharp shoulder to abrade the nipple, and coat nipples in grease, and use a spoke prep agent to lubricate and isolate the spokes and nipples, but the corrosion resistance of brass is better.
Another thing that happens with alloy nipples is that the shoulders can pop off, as in the pic below.
They are more susceptible to this with improperly sized spokes (see pic below)
but we've seen it happen (not on wheels we build, fortunately) on properly sized spokes. I can't definitively tell you what brand of spokes they were, all I can tell you is that it was wheels from two separate cross bikes, owned by team mates who'd gotten the wheels with the bikes. The spoke lengths were absolutely correct and the shoulders popped off one nipple on each wheel. The wheels were within their first season of use. No evident corrosion. You simply don't ever see that on brass nipples, and brass nipples are way more tolerant of slightly short spokes (not that you should undersize your spokes).
So should you get alloy or brass nipples? Our standard is brass. On balance, given everything, we think they are more right more often. If you are looking to reduce weight to the minimum possible, or want to add color to your wheels, you can use alloy. We offer it as an add-on customization option here. Just be aware that alloy nipples may have some longevity compromises.