I've smoked both. I love Flake Medallions and give it a grade of A. Bullseye Flake is similar, but I grade it B/B+.
I think the constituent tobaccos are the same or very similar. There are the cut sweet hay and stewed figs flavors and then you get that periodic hit of extra sweetness (from the cavendish centers?) and it is all very good. Why the difference in my opinion?
First, Flake Medallions are smoother in the smoking, with BEF being a bit harsh at times. Not really tongue bite, more a mouth/throat feel. Second, I think FM is a bit sweeter and richer. Third, FM seems to have a wee bit more of a perique pressence.
I suspect that Flake Medallions are aged Bullseye Flakes. that would explain why BEF smokes harsh in comparison and why the "young" Va isn't quite as rich or sweet, and thus, why the perique would not stand out as much. Perhaps. Or maybe there is a wee bit more perique in FM. Looks to be the same or very similar tobaccos.
Anyway, I aim to purchase more tins of FM at maybe one a month. However, I've a pound of BEF aging. I'll try it in a year and see what it is like. With any luck, it will be closer to Flake Medallions.
Hope this helps. Cheers,
TC