Just think about this: to move a table across the network
you can either (a) make a physical copy, and this includes
data, indexes, triggers, transaction caches, and whatever
the DBMS keeps in store for that table, or (b) copy just
the data as SQL statements or as exportable text, but then
the receiving DBMS should rebuild the indexes.
Instead, to calculate a CRC you have just a table scan.
Therefore you should compare the time needed to calculate
a SHA twice per record (one for the record and one to apply
it to a global SHA) versus the time needed to pass all the
above mentioned stuff over the network.
I put my bet on SHA. :)