Hey NicolasFSS,
Congrats on making it into the programs of your choice. To be honest, this decision needs to be taken by you by factoring your personal desires and concerns. To give you an idea as to what's different between HEC and LBS, I'd like to bring up the unique focus of the two programs.
1) HEC Paris is currently higher up on the FT rankings and is a well-renowned school in Europe whereas the LBS is not too far behind and is well-known around the world with a vast network of Alumni.
2) As you mentioned language should be a factor too, but considering the fact that the programs are entirely taught in English, it might be a worthwhile experience to explore a new culture and learn a new language. Such skills are appreciated by your future employers as it shows flexibility on your part.
3) HEC's program is an 18-month program with the option of a gap year to explore a specific business sector whereas LBS is a 12-month long program and is their flagship masters in management degree.
4) The HEC offers a wide variety of specializations and double degrees. It also has exchange partnerships with some very strong schools with the option of additional certificate programs sponsored by companies. LBS, on the other hand, relies more on its strong career services and has access to a large number of global corporations.
5) You should also look at some of the industries that alumni of both schools are in. It could help you making the right connections for your business even if you don't plan on joining corporates.
This is a very one-dimensional comparison focusing on just the academic aspect of these programs. You definitely should take into consideration factors such as sports facilities, location, food, accommodation etc, based on your interests and needs.
You can check out our review of the schools in the following links:
1) HEC Paris -
https://www.mim-essay.com/hec-paris-mim-review.html
2) LBS MiM -
https://www.mim-essay.com/lbs-mim-review.html