Hi
I am not a student at any of the two institutions but I am a Norwegian citizen and I have several friends currently studying at both of the schools so I can write my
personal opinions on the two.
I assume you are planning to go to BI in Bergen since you are comparing the two institutions. If not, Oslo and Bergen are two completely different cities and you should look into the cost of living and such if you want to live there for two years. Renting an apartment/unit in Oslo is very expensive, Bergen is expensive as well but it is easier to find less expensive apartments/units.
The Norwegian School of Economics (NHH) has always been the first choice for both undergraduate and graduate Norwegian business and economics students. The institution has a very high reputation (in Norway) and graduates generally earn more that graduates from BI.
It is also very important to remember that virtually any student get accepted to BI, if you pay you will get a place, whilst NHH (a tuition-free institution) is very selective and only choose the students they want. Most of my friends at BI are only doing there undergrad before either applying for graduate studies at NHH or going abroad (to Britain, Denmark, France or Italy).
NHH is also a member of CEMS so it is possible to take a part of your degree at other CEMS institutions (and you do not have to pay tuition fees). They also have exchange agreements with institutions such as HEC Paris, Bocconi, etc. I don't know how the exchange program at BI is, it might be better but I doubt it.
Non of them are bad, I have heard about both success stories and failures from both of the universities but I would dare to say NHH have a higher success rate.
I am planning to start on my Master degree next year and I will be applying to, among many, NHH but not to BI.
I can't comment on the comparisons with UK universities neither can I comment on individual courses, sorry.
Hope this helps a little bit, I think you will be very satisfied studying in Norway no matter which institution you eventually end up going to.