I was thinking awhile before weighing in. If the measure is competitiveness, my view is Kenyans and their businesses can carry their weight at any stage.
However when considering why Kenyan businesses seem to be dominant only in East Africa or COMESA, I looked at Nigeria. If you pick particular industries music, entertainment, banking etc it's clear that Nigeria has become a force in the continent north of SA.
My conclusion is that major limitation is size of Kenyan market. To really conquer, you need a good company in a large market making larger profits that spills over in the domination of smaller markets. South Africa, Nigeria, Egypt are doing it.
Hence it'll always be easier for Kenyan businesses to tackle EA markets as opposed to South Africa or West Africa for example.