Sig,
Again, most of this info comes from my mate on the A330 (I know people on both the Airbus and Boeing fleets). The A330 gets a good mix of Europe, ME and Africa. Euro layovers include Munich, Zurich, Newcastle, Athens and Nice. You hit every major city in the Middle East, India and Pakistan. In Africa you hit most of the cities on the East side as well as Durban, South Africa. You don't end up flying the ultra-long haul flights that you would on the 777 fleet (although Durban can be a long flight - I think 8-9 hours?). So, you get shorter, local flights (including the dreaded midnight turns to India) mixed with some medium-haul to Europe for the most part. My mate enjoys the variety of the routes. The A340-500 (which you might transition to after 1-2 years if you don't get bumped to the A380) flies to Australia, China and some European and West African flights.
As mentioned earlier, the A380 will be replacing some of the 777s on flights to the States in the future. The Airbus side will see the bulk of the growth with something like 90-120 A380s have been ordered - not sure if all orders will eventually show up on the tarmac. As a newhire on the A330 you can probably expect to be in this A380 seat in 2-3 years depending upon total time/experience/company need:
JetPhotos.Net Photo » A6-EDK (CN: 030) Emirates Airbus A380-861 by geo
In that case, you will get primarily long-haul flying (States, Canada, Asia, some Europe) and the associated fatigue/exhaustion. So, enjoy the shorter, local flights on the A330 while you can.