In 2014, according to Stanford’s admissions office, Harvard won 58% of the 214 kids cross-admitted with Stanford: https://stanford.app.box.com/s/y4abufqg66nte7uax6eq . It’s possible that’s changed in the past three years; I guess we’ll find out when Stanford publishes updated information.
Either way, though, the number of cross-admitted kids is only a little over 10% of all admits at both places, so the two schools are admitting overlapping but very different groups, and the difference between winning 58%-42% and splitting 50%-50% is 17 kids, or 3-4 freshman suites in Harvard Yard. If you interviewed literally hundreds of kids at both schools, you wouldn’t be able to tell which won more cross-admits.