My overseas employer accepted a Basic Disclosure, I didn't even realise there options other than the Basic Disclosure and I don't think they did either.
I forget the exact wording they used but I think they asked for a 'Criminal record check' and were fine with the Basic Disclosure. I got the feeling it was something of a box ticking exercise.
It may vary though especially when it comes to getting a visa because the embassy may be more familiar with the UK system than the employer.