I find that hard to answer in that context as it depends on what you spend most of your money on outside of basics and big corporations. Everyone's different. Thus as a whole I find it easier to say something like 80% of all the places that take Amex seem in my experience to take Diners. Put another way, for any given shop, it's more likely not to take Amex than taking Amex but not Diners.
I feel this makes sense because merchant fees for Diners are probably close to identical than those for Amex. So a place that takes Amex seems pretty stupid not to take Diners, in fact I actually find it absurd (particularly when you would think that Diners holders are probably pretty cashed-up, cluey people). I reckon it's often likely that they haven't been bothered getting a Diners merchant account set up because of lack of business acumen rather than anything to do with paying fees.
