The specific case you mention is covered by rfc6724:
10.5. Configuring a Multi-Homed Site
Consider a site A that has a business-critical relationship with another site B. To support their
business needs, the two sites have contracted for service with a
special high-performance ISP. This is in addition to the normal
Internet connection that both sites have with different ISPs. The
high-performance ISP is expensive, and the two sites wish to use it
only for their business-critical traffic with each other.
has two global prefixes, one from the high-performance ISP and one
from their normal ISP. Site A has prefix 2001:db8:1aaa::/48 from the
high-performance ISP and prefix 2001:db8:70aa::/48 from its normal
ISP. Site B has prefix 2001:db8:1bbb::/48 from the high- performance
ISP and prefix 2001:db8:70bb::/48 from its normal ISP. All hosts in
both sites register two addresses in the DNS
What it doesn't provide is automatic failover when a route goes down.
Multiwan failover is not part of the ipv6 specification (rfc2460)
The situation is the same as for ipv4, except that NAT is discouraged in ipv6 and so the same solutions we use in ipv4 would be a problem in ipv6.
The cleanest way to do automatic multi-wan failover would be to get an ipv6 block and setup BGP with both ISPs, but that might be a bit overkill for a small setup. The same applies to ipv4.
The cheap option in ipv4 was to do NAT and have a router choose which wan link to use. The equivalent in ipv6 is NPTv6 with ULA on the inside with some advantages over ipv4's NAT.
The way applications will handle the failover from one link to another will depend on the application and the way it's built. The server the application was talking to will suddenly be talking to a different address with a different network prefix.
Applications talking HTTP likely won't experience issues. Applications talking SSH will have their connections break.
So to sum up, no, IPv6 doesn't have any magical failover/roaming solution that will work out of the box for all applications transparently.
PS: I've seen people talk about using router preference as a means to achieve failover in your original scenario, but I have no idea whether that would work. Even if it did applications would still have to take care of some aspects (ssh connections would still die)