Double Degree or LBS/LSE

Hi!

I'm a recent graduate struggling with a doubt about his university career and you could really help me with a simple opinion.

I have completed my bachelor in Economics and Management with the best GPA possible, studying in 3 languages, having leadership roles in academic associations, taking part in different extracurricular activities along the way, and so on. However, I now find myself at a crossroads.

I was admitted to a double degree offered jointly by ESSEC and Bocconi, during which I would study for 2 years on 4 campuses (Milan, Singapore, Mumbai, Paris) and at the end of which I would obtain a Master in Management from both universities. (https://www.unibocconi.eu/wps/wcm/connect/Bocconi…)

However, with my GMAT and my average, I could also aspire to be admitted to the 1-year long Masters in Management offered by LSE and LBS. In this case, while waiting to apply, I would be forced to take a gap year to fill with internships (risking, due to the unfavorable economic situation, to end up in roles that are not particularly formative).
My question, therefore, is the following: my goal being consulting, is the high internationalization of the double degree to be preferred to the greater prestige of London schools, given the fact that the latter would be preceded by a year of uncertain work experience?

I have tried to be as synthetic as possible, in case you have questions to better answer feel free to ask!

Thank you very much in advance for your time!