Sorry to say I think they're all about as bad as each other.
Before I went to Uganda, I'd heard that Horizon were one of the better companies, but the Horizon bus we caught from Mbarara to Kabale was hours late, decrepit (admittedly it was a replacement bus for one that had broken down - hence the lateness...) and just as bad driving as the rest.
Link had comfortable newish buses and the scariest drivers, but this may have been down to being on good roads: it's better when the road is not so good because they have to drive a bit slower.
The Post bus was very nice and left exactly on time, but still drove recklessly.
In order of feeling safe and fairly confident of reaching my destination in 1 piece, I'd choose minibuses or matatus over buses (at least you can see what's happening!) and buses over shared cars (you can see, but being wedged into a saloon with 10 - or more - others, including a couple sharing the driver's seat, does not inspire confidence.)
Also more than a few of our shared taxi drivers seemed to have a death wish, not only driving very fast but mostly on the wrong side of the road.
Really, you might as well just take the first transport that comes along, I doubt it makes very much difference, and often there is no choice anyway.