Thank you very much for the bugreport.

How do you think we may resolve it?
If said for /usr/include/ImageMagick-6/magick/magick-baseconfig.h (and similar for /usr/include/ImageMagick-6/magick/version.h) I could patch ImageMagick to place files like /usr/include/ImageMagick-6/magick/magick-baseconfig-<arch>.h and then include appropriate where it was used before...

But /usr/bin/MagickWand-config seems correct binary name. I personally do not think it is good to make there to copies and then patch all who relies on that path.
What you think? Do we have any guidelines for that? I've found so far only that draft: https://fedoraproject.org/wiki/PackagingDrafts/MultilibTricks

For MagickWand-config, just patch out seting PKG_CONFIG_PATH=.  It's unneeded and likely the source of the conflict.

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Error: Transaction check error:
  file /usr/bin/MagickWand-config conflicts between attempted installs of ImageMagick-devel-6.8.8.10-9.fc22.i686 and ImageMagick-devel-6.8.8.10-9.fc22.x86_64
  file /usr/include/ImageMagick-6/magick/magick-baseconfig.h conflicts between attempted installs of ImageMagick-devel-6.8.8.10-9.fc22.i686 and ImageMagick-devel-6.8.8.10-9.fc22.x86_64
  file /usr/include/ImageMagick-6/magick/version.h conflicts between attempted installs of ImageMagick-devel-6.8.8.10-9.fc22.i686 and ImageMagick-devel-6.8.8.10-9.fc22.x86_64

PKG_CONFIG_PATH=/usr/lib64/pkgconfig:/usr/share/pkgconfig there. Why you think it is not correct? And could you please be nore verbose, what result are you expect? What should happen with aforementioned binary?

It's not needed (that's the default search path for pkg-config) and it causes the conflict because it will be set to PKG_CONFIG_PATH=/usr/lib/pkgconfig:/usr/share/pkgconfig on 32-bit.  The files must be identical to not cause the conflict.

But /usr/bin/Magick-config files already identical in both packages.

It's /usr/bin/MagickWand-config that's the problem.

ImageMagick-6.9.2.7-1.fc23 has been submitted as an update to Fedora 23. https://bodhi.fedoraproject.org/updates/FEDORA-2015-7faffa80f1

ImageMagick-6.9.2.7-1.fc22 has been submitted as an update to Fedora 22. https://bodhi.fedoraproject.org/updates/FEDORA-2015-3a5cebb105

Conflicts appear to be fixed.  Thanks.

ImageMagick-6.9.2.7-1.fc22 has been pushed to the Fedora 22 testing repository. If problems still persist, please make note of it in this bug report.
If you want to test the update, you can install it with
$ su -c 'dnf --enablerepo=updates-testing update ImageMagick'
You can provide feedback for this update here: https://bodhi.fedoraproject.org/updates/FEDORA-2015-3a5cebb105

ImageMagick-6.9.2.7-1.fc23 has been pushed to the Fedora 23 testing repository. If problems still persist, please make note of it in this bug report.
If you want to test the update, you can install it with
$ su -c 'dnf --enablerepo=updates-testing update ImageMagick'
You can provide feedback for this update here: https://bodhi.fedoraproject.org/updates/FEDORA-2015-7faffa80f1

ImageMagick-6.9.2.7-1.fc23 has been pushed to the Fedora 23 stable repository. If problems still persist, please make note of it in this bug report.