I think your distinction on negativity and positivity might not be accurate. There is no reason one could not say "the company was fated for success", or "it was his ultimate destiny to die in a car accident."
The two are largely synonymous, but if there is a distinction to be made, I believe it is to do with the degree to which one believes free will plays a part.
Fate implies that the results were inevitable regardless of the actions of the people or entities involved. A company fated for success can do no wrong, it was always "in the stars" that they would become that way. When you say someone ended up at their fate, you are most likely talking about how it didn't matter what they did. Even though they were a successful rock star and had everything going for them, they still died in a plane crash. It was their fate.
Destiny implies some amount of direction and action on the part of the people or entities involved. Your destiny is a path laid out for you, but you still have to walk it. When you say someone was destined to be famous, you are acknowledging that they not only had the talent but that they promoted themselves and practised and networked and did whatever it took to get noticed.
In other words, you can sensibly say "it was his fate to be in a car accident" and "it was his destiny to be in a car accident", but in the first case, no matter what he did that car accident was going to happen to him. In the second case, his actions, by driving recklessly perhaps, it was inevitable that eventually the accident would befall him.
Confusion reigns over these two terms, of course, especially because both are used in a hyperbolic way. There is no such thing in reality as a company that is either fated or destined for success. Any company can fail at any time for any number of reasons. But, in retrospect, especially when talking about massively successful companies that seem to have done everything right from the get-go, people throw about fate and destiny as if they had some literal weight, and in the process blurring the lines between the two.
Probably the clearest line of distinction is in their negative forms. You can miss your destiny, but not miss your fate. "She was destined for success but rested on her laurels, and thus did not make it," is a sensible thing to say. However, "she was fated to die that day but didn't" seems strange (to me). If she didn't die, then it couldn't have actually been her fate.