My wife and I were having a big debate about which fridge to buy.
My wife and I argued about what kind of refrigerator we should buy.
ーMy wife and I were having a big debate about which fridge to buy.
「妻と私はどの冷蔵庫を買うかで大きな議論をした」
to have a big debate about で「…についての大きな議論をする」
about which fridge to buy で「どの冷蔵庫を買うかについて」
ーMy wife and I argued about what kind of refrigerator we should buy.
「妻と私はどの冷蔵庫を買うべきかについて議論した」
to argue about で「…について議論する」
about what kind of refrigerator we should buy で「どの種類の冷蔵庫を買うべきかについて」
ご参考まで！
カナダ 
