Several, actually.
For starters, I happen to believe it's better for readability. Another thing is, the regex modifiers "come with it". So you can include things like the 'x' modifier right along with the regex; if you're using a string as a regex, on the other hand, you have to remember which modifiers you need when you finally decide to use it in a match.
Also, even though it doesn't show in this example, qr// is more efficient as (IIRC) it pre-compiles its regex before matching: i.e. you can build the regex once and use it several times. I use the qr// operator this way to make my regexes "modular".
Anyway, you already know that I've been wrong about efficiency before :), so please correct me if you have a different say on the matter. I'm here to learn...