This is because the 'max_allowed_packet' stting on the two servers are different. There are BULK INSERTs too large for the server where you restore. I have writen a bout the problem in our Blog:
http://www.webyog.com/blog/2009/08/10/mysql-server-has-gone-away-part-1-max_allowed_packet/
Os raise the setting by entering the line
Code:
max_allowed_packet = 16M
.. for instance in the server configuration file (my.ini/my.cnf) and restart the server for the change to take effect. Or define a BULK size not too large when exporting.