Doesn't seem like you'd really need twins to conduct this test yourself - just send in two samples from the same person under different names.
I don't know why the 'relatively' small difference between the twins ethnicity profile on the 23andMe occured but the much larger difference between 23andMe and the other companies is due to them each using different databases to compare them with. I had my dna tested with Ancestry last May and their ethnic profile picked up my Irish/English heritage correctly but much to my surprise gave me 5% Iberian peninsula ancestry. It turns out Ancestry were using the dna of just 3,000 people worldwide to breakdown peoples dna into geographic regions. When they increased this database to 15,000 people and gave me an updated profile the Iberian connection had disappeared. In fact just last week they updated the Ireland database to include over 90 Irish geographic regions and they correctly (according to my own research) placed my ancestry as coming from Co Sligo, Co Antrim and Co Down. I think we are still in early days with ethnic/geographic profiling as the twins results show but it's definitely improving.