In another question this example of semicolon usage is given:
When dinosaurs agree on something, they often high-five one another; dinosaurs are all about high-fives.
However, I have also seen the following style before, where the second part acts like a regular sentence with the first word capitalised:
When dinosaurs agree on something, they often high-five one another; Dinosaurs are all about high-fives.
I can see the reasoning: the semicolon is bridging two sentences. Which one, if any, is correct? Is it simply a style issue?