Strictly speaking, there is no difference in meaning; so the choice comes down to convenience.
Here are several factors that could influence your choice:
- House style: Some groups of developers already use one convention or the other.
- Client-side requirements: Will you be using quotes within the strings? (See Ady's answer.)
- Server-side language: VB.NET people might choose to use single quotes for JavaScript so that the scripts can be built server-side (VB.NET uses double-quotes for strings, so the JavaScript strings are easy to distinguished if they use single quotes).
- Library code: If you're using a library that uses a particular style, you might consider using the same style yourself.
- Personal preference: You might think one or other style looks better.