The Vilna Gaon famously held that there is no proof from Chazal that the obligation of tefillin applies on Chol HaMo'eid. In Bi'ur HaGro on Shulchan Oruch Orach Chayyim 31:2:2, he refutes the most famous proofs that the obligation of tefillin does apply on Chol HaMo'eid. One of those proofs is a Mishno, namely Beitzoh 1:10. There are two versions of this Mishno - the Bavli version, which says:
"One may send clothes... provided they are necessary for the festival"
and the Yerushalmi version, which says:
"One may send clothes... even though they are not necessary for the festival."
All those that use this Mishno as a proof for the obligation to put on tefillin on Chol HaMo'eid use the Bavli version, and so to refute this as a proof, the Vilna Gaon says that the correct version is the Yerushalmi version.
It is well known that the Talmud Bavli has been preserved far better and is far more reliable with regards to different versions of texts than the Talmud Yerushalmi (see Tosfos on Yevomos 104a and Chovos Yo'ir 23:4).
So, my question is: Why does the Vilna Ga'on decide to use the Yerushalmi version of Beitzo 1:10 instead of the Bavli version?