Should the second part of a semicolon-separated sentence be capitalised?

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?

Solution 1:

As you say yourself, the semicolon is bridging the gap between two sentences; they become one.

Wikipedia is exceptionally succinct on this:

English usage

Semicolons are followed by a lower case letter, unless that letter is the first letter of a proper noun.

Solution 2:

The Chicago Manual of Style (6.57 - 6.62) uses a small letter after the semicolon, e.g.

Mildred intends to go to Europe; her plans, however, are still quite vague.