One of the advantages of dual stacking is that you no longer depend on one protocol. If part of your network dies and takes out IPv4, there’s a chance that IPv6 will still work, allowing you to log in and fix the problem.
This may seem like a rather slim chance, but I’ve seen a few instances of it. In one case the IPv4 egress router was so busy generating ICMP messages that it couldn’t forward packets any more. The IPv6 router was uneffected by the problem, as the ICMP messages were in response to a worm, and continued to allow access to those using IPv6.
More recently, I’ve seen a problem with a etherchannel between two Cisco boxes, which resulted in IPv4 packets between certain pairs of machines being dropped. Getting this sort of problem resolved takes time, and we were able to ask users to use IPv6 as a workaround until the problem was resolved.
Of course, the opposit has happened too - an ethernet card in an IPv6 router failed while IPv4 continued merrily on its way.