They both mean 'game' or 'contest'. Are they interchangeable or is there a difference?
They have different meanings. 試合 means "game", "match". I think the meaning of 競技 is close to "sports" rather than "game" and "match".
For example, we say サッカーの試合を見た, but we rarely say サッカーの競技を見た. We say サッカーは団体競技だ、but we don't say サッカーは団体試合だ.