An important difference is that cars are a purchase with an expected eventual value of close to zero where as houses are typically seen as an investment with a goal of being to eventually sell it for more than you paid for it.

This means that car payments are more of a cost of ownership and house payments are more of a reoccurring investment.

As long as the house is actually a good investment, being able to afford the down and monthly payments is the most important thing. Rather than spending vs saving/investing, the trade-off becomes more of investing in real estate vs investing in something else.