It's hard to categorize, because how do you define the boundaries of a "tank battle?"
Ok, that said,
, here are the ones I am familiar with:
Largest tank battle in history: Sinai 1973
Largest Tank Battle of WWII: Prohorovka 1943
Largest Tank Batte on the Western Front: Arracourt 1944
Largest Tank Battle including British Troops: Operation Goodwood 1944
Even the Russians themselves scoff at Prohorovka being the biggest battle, as other engagements saw over 1,500 Russian tanks involved all in one operation.