We are looking for something that can compete with this graphics card and is a bit cheaper ASRock Challenger D Radeon RX 6600 XT 8GB Video Card
Well, a used 5700 XT or used 2060/2060 Super will compete with it, but those are naturally going to be riskier. It's not really cheaper, you're just paying some of the cost in risk instead of cash.
Outside of that, not really. AMD generally makes the less expensive GPU in terms of performance per dollar.