My gut feeling based on your description says go with UVA, but you should validate this. Really, it depends on a number of criteria.
Firstly, I would also challenge that "grades are of the utmost importance" for consulting - at least in the UK, unless you do exceptionally well (e.g. top of your class) or very poorly, the grades don't matter that much. Or let me rephrase - while having an excellent GPA certainly won't hurt your chances, it also definitely won't be a "make it or break it" criteria. So don't choose a place based on fact you think you can get better grades
If you want to work internationally - then go with the one with the better international rep. - the more likely it is that the office you are applying to at least knows ofthe uni., the better.
What matters much more than grades is the quality of the uni and the work experience & extra-curricular activities you have. Do you know if one of the two unis has more opportunities for getting involved in societies, consulting clubs, etc., or provide opportunities to do full-time internships or part-time work? This would be a potential deciding factor in choosing between the two.
Finally, have you looked into alumni from these two unis, and where they tend to place? Are there an equal number of people at McKinsey/Bain/BCG from both, or is there drastically more from one vs the other? This could be an insightful lens, as you should probably validate your assumption that "they are roughly on equal standing locally".