I don't think there is any significant difference between "" and ''. Consider that the metachar \ is still checked in single quoted strings, this means that both types undergo some char check. I find '' to be easier to read, which is a good enough reason to use it (in my book).

Another point, however, is that I generally encourage people to put the constant first in a comparison. This may seem odd, because its the reverse of how we like to read it, but it results in fewer typos of = versus == type. Really this is the only place it matters, but how often have you tweaked a >= into an = or tweaked an eq into an = ??? So I would check that ( '' ne $teststring ). Also, you know that '' is the equivalence of false. (Of course, so is "0", which is why you would want to be explicit.)