why <br /> and not <br/>?

If I recall correctly it's simply because some older browsers had problems with a self-closing tag without a space before the slash. I doubt it's an issue nowadays, but a lot of developers (myself included) got into the habit of including the space.

Edit: Ah, here we are:

http://www.w3.org/TR/xhtml1/#guidelines

Include a space before the trailing / and > of empty elements, e.g. <br />, <hr /> and <img src="karen.jpg" alt="Karen" />. Also, use the minimized tag syntax for empty elements, e.g. <br />, as the alternative syntax <br></br> allowed by XML gives uncertain results in many existing user agents.

Some older browsers didn't parse the element correctly without the space, so most web developers use <br />. I don't remember which browsers offhand, but I believe they're just about extinct.

EDIT: The browser was Netscape 4.

w3c specifies this as the grammar:

EmptyElemTag       ::=      '<' Name (S Attribute)* S? '/>'

That means open bracket, a name, a number of (space and attribute) tokens, an optional space, a slash, and an end tag. According to this, both are correct.

There is no right way in XHTML. They are formally identical in XML. Whitespace is not significant in that location.