To me, the answer seems very simple, and i can't imagine it ever being different: Practice with whichever ball will be used at the tournament you are preparing for.
It seems so obvious, yet i often see players - including very good players - practicing with a ball that is different from the one that will be used at the competition. Even during the day of competition, i see players warming up with an orange ball when the tournament ball is white. In my opinion, this is poor preparation.
It might be a hassle to get the precise ball that will be used at the tournament, but you should be able to come close. At least use a ball that's the same color, made in the same country, of the same construction, and now, made of the same material.
(Ideally, you should be training in conditions as similar as possible - same type of table, similar flooring, time of day, altitude, etc. Some of these are hard to achieve, but getting the same type of ball shouldn't be that difficult.)
Tournament directors in domestic competitions have always been required to state the brand and color of the ball that will be used. Now they are also asked to clearly state whether it will be a celluloid or non-celluloid ball. But if you're not sure which ball your upcoming tournament will be using, you need to ask them.
If you play internationally, the ball that will be used is pretty much predetermined:
- ITTF Junior Circuit events prior to the Youth Olympic Games - Butterfly *** celluloid, usually white
- Youth Olympic Games - DHS *** celluloid, probably white
- ITTF Junior Circuit events after the Youth Olympic Games - Butterfly 40+ *** non-celluloid, white
- ITTF World Tour events - DHS 40+ *** non-celluloid, white
- North American Championships - Double Fish 40+ *** non-celluloid, white
- World Championships - Butterfly 40+ *** non-celluloid, almost certainly white
What about US tournaments?
Tournament directors can choose any approved ball as their tournament ball, and both celluloid and non-celluloid balls are approved. In theory they could even use ball X for some events and ball Y for other events. I cannot predict which ball a particular tournament director will choose, but put yourself in their shoes: If you were a tournament director, and you wanted to maximize player attendance, which would you choose?
At the moment, most US players are still using celluloid at their clubs, and it would be somewhat risky for a local tournament director to host a tournament tomorrow using non-celluloid balls. Non-celluloid balls are not sold by all major brands yet, and bulk cheap non-celluloid practice balls are even harder to find. Things will probably change as the availability of non-celluloid balls improves.
One more question that people ask: Should i buy balls from auction sites or department stores? To that i respond: If you were a ball manufacturer that produced several different grades of balls, where would you send your best ones - to the person running online auctions, to the department store, or to the specialist table tennis store?