Well no to all of the above. The main reason the Virginia class has a larger crew is has three shifts like other US-UK nuclear submarines. Whereas Collins like most DE boats only has two shifts. One of the issues in favour for domestic design of a SEA 1000 boat is the ability to provide a three shift crew.Some of the it is likely due to the differences in crewing doctrine between the US and allied navies. The US tends to have crew dedicated to damage control while other navies (RN, RAN, etc) seem to have damage control performed by crew as an additional function.
I agree that the USN does seem to use less automation than others, which could cause crew requirements to be even higher,