I would suspect that your regular chives will be more vigorous and may crowd out your garlic chives. The regular chives I've grown are far more vigorous than the garlic chives I've grown - which gave up the ghost during the last winter. As far as them crossing, I don't know. But I suspect their bloom times may not be in sync and that would make crossing them impossible. My garlic chives where always a fair bit later in coming up than the other chives and that's why I think the bloom times may be different.

FataMorgana