The Nigerian economy is massive, but there is no way its 10 times Kenya's. My guess is that they are about 6-8 times larger than Kenya.
There big forex earner is obviously Oil (2m bpd), but an even greater driver of their economy has to be their production for own consumption. Imagine making 100 million Agbada's (the west African wear) per year, the textile industry must be massive and I am sure most of it is off the grid. That can't be matched anywhere else in Africa.
Their entertainment industry is also very impressive, how many of those garbage movies do they make per year, and their music now is becoming the official african tune. Add in diaspora remmitances etc. I am sure their diaspora remmitance is huge compared to other African countries.
Kenyans are very poor spenders compared to the etravagant nigerians who will spur economic growth through consumption.
From my observations, an average Nigerian will consume 2X the amount of food consumed by a Kenyan per sitting and possible much more per day coz i bet they have less incidence of hunger. Don't forget that a large proportion of Kenyans are hungry and ain't got nothing to eat more than twice per day.
However, if you visited Lagos, you would be distressed by the diorganisation, every hovel has a generator.
I however think most of these GDP's are driven by the ease of computing them, e,g its easy to count the oil exports made, you then apply its multiplier effect to the economy and voila, you have a legitimate GDP estimate, akin to Nigeria or Angola.
Come to the case of Kenya and you have to work out the production for each household and sudenly you are left with the responsibility of counting beans, nobody wants to get into that so what them folks at the World bank do is to estimate and move on. It does not help that our gava is not interested in hard work either so will not bother to correct the obvious errors.
"The purpose of bureaucracy is to compensate for incompetence and lack of discipline." James Collins