As far as I can tell, there is no difference between the 2 operations and both seem to achieve the same thing. From this I assume that bulkadmin is just a wrapper around the ADMINISTER feature although I'd be interested in knowing (as I couldn't find out) if there are other permissions the server role gives you.
Lets look at the example (running on SQL2008 SP2)
-- create some test logins
CREATE LOGIN [DOMAIN\user1] FROM WINDOWS
GO
CREATE LOGIN [DOMAIN\user2] FROM WINDOWS
GO
-- lets impersonate a user
EXECUTE AS LOGIN = 'BARRHIBB\user1'
GO
-- and check the server permissions
SELECT * FROM sys.server_permissions
GO
SELECT * FROM fn_my_permissions(NULL,'SERVER')
GO
-- does the user have bulk op permissions?
SELECT has_perms_by_name(NULL, NULL, 'ADMINISTER BULK OPERATIONS');
GO
-- lets go back to being a superuser
REVERT
GO
USE MASTER
GO
-- how about if we just grant administer bulk operations to the user?
GRANT ADMINISTER BULK OPERATIONS TO [DOMAIN\user1]
GO
-- lets impersonate that user
EXECUTE AS LOGIN = 'DOMAIN\user1'
GO
-- and check the server permissions
SELECT * FROM sys.server_permissions
GO
SELECT * FROM fn_my_permissions(NULL,'SERVER')
GO
-- does the user have bulk op permissions?
SELECT has_perms_by_name(NULL, NULL, 'ADMINISTER BULK OPERATIONS');
GO
-- can the user grant other users to be bulky people?
GRANT ADMINISTER BULK OPERATIONS TO [DOMAIN\user2]
GO
Msg 4613, Level 16, State 1, Line 2
Grantor does not have GRANT permission.
So lets see what happens with the server role:
REVERT
-- remove the users permissions
REVOKE ADMINISTER BULK OPERATIONS TO [DOMAIN\user1]
GO
-- now add the user to the bulk admin role and check permissions again
EXEC MASTER..sp_addsrvrolemember @loginame = N'DOMAIN\user1', @rolename = N'bulkadmin'
GO
-- lets impersonate that user
EXECUTE AS LOGIN = 'DOMAIN\user1'
GO
-- and check the server permissions
SELECT * FROM sys.server_permissions
GO
SELECT * FROM fn_my_permissions(NULL,'SERVER')
GO
-- does the user have bulk op permissions?
SELECT has_perms_by_name(NULL, NULL, 'ADMINISTER BULK OPERATIONS');
GO
NB: The main difference here is that the permission has not been explicitly granted but it is an effective permission.
-- perhaps with the server role the user grant other users to be bulky people?
GRANT ADMINISTER BULK OPERATIONS TO [DOMAIN\user2]
GO
Msg 4613, Level 16, State 1, Line 2
Grantor does not have GRANT permission.
So it seems that the bulkadmin server role doesn't offer any "admin" from a security point of view which begs the question, just why would you add a user to this role rather than just explicity grant them the permission through the GRANT statement (or vice versa)?