I wonder the difference between them. As both of them claim to test on the problem-solving skills and critical thinking.
As they were created by the same company and there is really no such thing as "critical thinking, Cambridge- or Oxford-style", I'd assume they'll be pretty much the same, even though the actual questions may not be identical.
I may well be wrong but I can't imagine there being any difference in the Multiple Choice test (other than actual questions) - I'm not sure whether or not the Cambridge TSA has the same Essay portion, however.