Why is XOR preferred over XNOR? The XOR operator seems to be a frequently used building block inside many cryptographic primitives.  As far as I can see, its most desirable properties seem be that for the XOR of two bits $a\oplus b=c$:


The information is preserved.  Either $a$ or $b$ can be recovered from $c$ and the other bit.
The information is hidden.  An adversary can not learn anything about $a$ or $b$ from $c$ alone.


Neither AND nor OR has these properties but XNOR does.  It seems like any cryptographic application using XOR could be constructed equivalently with XNOR, without incurring any loss in security.  One possible reason to prefer XOR might be that XOR is equivalent to addition modulo 2, whereas XNOR would be addition plus 1 modulo 2, but this seems to be entirely mathematical, and I'm not sure if it actually results in any additional hardware complexity in practice.

Is the choice of XOR then an arbitrary one, made for historical reasons, or is there any tangible underlying motivation for using it over XNOR?
$\operatorname{XOR}$ is similar to addition when working on Booleans; by contrast, $\operatorname{XNOR}$ is not a group law if we want to use $0$ as neutral.
Economy for extension: we can build a 3-inputs $\operatorname{XOR}$ from two 2-inputs ones; we can't for $\operatorname{XNOR}$.
Economy for making one: we can build $\operatorname{XOR}$ with four identical 2-input $\operatorname{NAND}$, but that can't be done for $\operatorname{XNOR}$. The construction goes:


$z\gets(a\;\operatorname{NAND}\;b)$;
$x\gets (a\;\operatorname{NAND}\;z)$;
$y\gets(b\;\operatorname{NAND}\;z)$;
$c\gets (x\;\operatorname{NAND}\;y)=(a\;\operatorname{XOR}\;b)$.



Update: the later argument works only because/when $\operatorname{NAND}$ is cheaper, faster, or/and less power-hungry than $\operatorname{NOR}$. That indeed was the case in TTL logic: that source shows 4 NPN transistors for $\operatorname{NAND}$, including one with two emitters, versus 6 for $\operatorname{NOR}$. The same holds for RTL logic made from PNP transistors, which used to be popular when these where made using germanium. However, RTL logic using NPN transistors (typically, on a silicon Integrated Circuit), which favors $\operatorname{NOR}$, has also existed. Famously, the Appolo Guidance Computer was built from 3-inputs $\operatorname{NOR}$ gates, two per IC.