I presume by MC you mean Management Consulting - well, INSEAD is traditionally considered a bit better than LBS in this field. Don't really know how those schools are for non-profit. Typical (albeit simplified) Top-Europe b-school perception is "LBS for finance, INSEAD for consulting and IMD for industry".
I know there are endless arguments which school is better, LBS or INSEAD. In my opinion, their quality and reputation are comparable, so the choice really depends on your personal preferences - do you need a 2-year or 1-year MBA? where would you be a better fit? where would you like to work? where would you like to live and study - UK or France/Singapore?
If you really not sure, you could apply to both
Also, INSEAD has two intakes, so you might consider the possibility to apply for Jan 2010.
Anyways, good luck to you!