Info from 2010 : If you stick on the main road you will find asphalt road nearly all the way. Each metter from cape town to the tanzanian kenyan border is asphalted (though Tanzania, Malawi, Mozambic), you will be amazed (road have been financed and build by international charities). You will only do few hours in dirt tracks in the whole trip.
So from the Tanzanian border to Naeroby you will find a dirt road, but you don't need a 4x4 to go there, if you drive slowly (might be wise to avoid the rainy season though, but even, no big deal, it's an highway).
You will then find asphalted road going north Kenya, but then the first (and only) tricky passage from Kenya to Ethiopia, few kilometers. Westerners usually regroup to pass these kilometers in convoy, you just need to pass between tribal fights. These tribal guys might seem impressive, (they got weapons) but not that dangerous (you will find is this latitude cultures that value honor, unlike the south where they value money).
You won't have difficulties finding other westerners travelling, along this long road is a highway of tourist. (You will see all the way these rich guys with their amazing 4x4 over equipped and ready to cross the martian desert !)
I don't know about asphalt in Ethiopia, but it doesn't look the big deal but... you might be stoned all the way by kids and teenagers, and insulted all the way, sometime by adult (a local Ethiopian custom).
As long as you are not islamophobic and the kind of arrogant-westerners North Sudan will be your easiest part. North Sudanese were the most friendliest I met on his road (from cape town to the western culture). They are extremely poor but if you come from the south they will be the first African to see in you something else than a dollar with legs (they don't beg), and to don't try to take advantage of your misfortune which, coming from south will seem extraordinary. (Some tourist find this country difficult because they can't buy these people dignity, impose their culture or use their financial power to do whatever they want. The westerner touristic standard "disco, alcohol, cheap sex & drug" is more difficult to find in this country than most of African countries). These guys are also corrupted, but less than in the south.
You will need to take the ferry with your car from Wadi Halpha to Aswan (no choice, it's forbidden to go by land).
Egypt was (and still is) a dictatorship and a military state, you may have to bride policemen and army to make it through the thousand check points you will face. But asphalt all the way up.
((Uganda is asphalted until its border with south Sudan, but south Sudan is a place you want to avoid (bad road, aggressive people, weapons, tribal war, bandit, anarchy). ))
Globally your biggest difficulty won't be the road state at all (you could do it with any cheap city car, easy, even passing through secondary roads, dirt tracks are not that bad, even at rainy season. Look at some picture on google to see african cars/buses!). Your biggest difficulty won't be either about those exotic stuff people say about Africa (lions, mosquitoes and stuff) but the people(✲), and your skin color —if you are white (or "whiter"). People will assume you are incredibly rich (just because of your skin pigmentation) and will try all the way (bellow the Sahel) to take advantage of you (even the richer than you). It's not the big deal if you are rich and ready to bride all the way up (or down) but it might cost you a fortune (literally) on backshish depending on your patience and commercial skills.
Using local transportation will be definitely much less troublesome much much cheaper (especially the visas!), even if you use (relatively) luxurious way to travel. Local transportation seem (to me) also much safer, and much much less troublesome because you will waste much less time with the African corrupted bureaucracy and you will, at least avoid being extort by military and policemen —among others— who will carefully watch you from every corner to "fine" or "tax" you for anything they might think on the moment you will pass.
(✲) Bellow the Sahel: remember that there is "nothing wrong" since things happens for a reason. These people were (and are still) living very differently few years ago (their social system), and thus think very differently. If you plan to do something more interesting than just driving from one touristic attraction to another and step out of your car without trying to run away from locals, you will find within social interaction the most impressive things you will ever see. But be prepare for a huge and tough psychological gap. If you cross Africa to hunt for cliches (such as wild life), you might be disappointed —unless you pay for it.