It's not that one MBA or another prepares best for consulting. Consulting is all about learning by doing. Moreover, INSEAD is a 1-year program and you don't really have a lot of time to study taking into account networking and all the recruiting activities.
What might be different:
- Availability of the on-campus recruitment
- Higher chances to get a job offer at Insead / LBS because of the targeted hiring
What you can do? Get a referral:
- Either from your classmates ex-consultants who can recommend you to on-campus recruiters
- Or from any consultant working at these companies globally