I'm familiar with the fact that theoretical formulae like Van der Waals equation are based on already known theory and are very frequently simplified (some equations don't include interactions between molecules for example) while the purpose of empirical equations (like polynomial equations) is just to follow experimental measurements even if it doesn't make any chemical or physical sense.

Which of these yield more accurate results (compared to reality)? What are the upsides and downsides of each group? Which are more universal? Which would require less compound-specific data (constants) to use it?

I'm familiar with the fact that theoretical formulae are based on already known theory and are very frequently simplified (some equations don't include interactions between molecules for example) while the purpose of empirical equations (like polynomial equations) is just to follow experimental measurements even if it doesn't make any chemical or physical sense.

Which of these yield more accurate results (compared to reality)? What are the upsides and downsides of each group? Which are more universal? Which would require less compound-specific data (constants) to use it?

Edit: Removed van der Waals equation as an example of theoretical equations since, as pointed out by others, it's actually an empirical equation.