I would look at the "will inherit" as a future instantaneous action, while "will be inheriting" as a future action in progress. They will often be used interchangeably and mean virtually the same thing. There are some cases, when it sounds weird to not refer to the action as a process. For example, with regard to watching TV. I will be watching TV tomorrow night, so I will not be available. CORRECT I will watch TV tomorrow night, so I will not be available. (This makes it seem like the person is going to watch TV tomorrow on purpose in order to not be available to do something else because they want to avoid participating in some other activity.) I'm going to be watching TV tomorrow, so I'm not going to be available. CORRECT (same as first) So in general, actions that are more seen as a process or that take place over a period of time, will slightly be better suited to a be + present participle form. Again though, most of the time they mean almost the exact same thing. Here are some more examples: I will be cooking tomorrow. (I will be in the process of cooking tomorrow.) I will cook tomorrow. (statement that I plan to cook tomorrow) He will be speaking at the event tomorrow. (he will speak over a period of time tomorrow) He will speak at the event tomorrow. (at some point tomorrow, he will speak) The train will be arriving shortly. (portrays the arrival of a train as a gradual process of slowing down to a stop) The train will arrive shortly. (portrays the arrival as a quicker more instantaneous action) I will be writing an essay, so I won't have time. (same as TV example)

not much difference

the same thing

I don't know how helpful this will be but as a native English speaker, those two sentences seem to be essentially the same. In another context one might be more fitting than the other, but from my own view there is hardly anything to differentiate them. I hope someone else can provide a more detailed answer~!