How do these two compare when it comes to applying to the more prestigious institutions in the US? Can an excellent GPA considerably make up for having graduated from an average undergrad school? Or does the school carry a lot of weight?

Would this vary from school to school when you're applying, or is it fairly consistent? Thanks.

Take a look at https://www.hbs.edu/mba/admissions/class-profile/Pages/undergraduate-institutions.aspx. I'd say 95% of these are above average in their own countries. However, few of these will have below-average grades. Prestigious schools generally recruit people where all the key variables are above average. Undergraduate schools are a good indicator of long-term success.

Prestigious schools generally recruit people where all the key variables are above average.

Yes, and that's especially the case if you are looking for financial support or in an over-represented applicant group in the pool (e.g an Asian male).