Which shows you can't always trust the internet, John.
I have both the Russian and the French variety of tarragon in my garden in Oslo, the first one is much taller and more vigorous, but it isn't too difficult to keep it under control. When it is fresh, the taste of the Russian tarragon is OK, but there is no flavour when it is dried. The flowers are inconspicious, and does produce seeds, while the French variety is totally sterile, I have never seen any flowers, but it is easily propagated by divison.
It would be interesting to try to grow the Mexican tarragon in Greece, I have never seen or tasted this one. We have just prepared a small vegetable patch which is ready to be planted next spring. Did you grow it from seeds?