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No.  Really, all eggs taste like, well, eggs!
There are subtle differences between different kinds of eggs.  Duck eggs taste "richer" than hens eggs as a rule.  But, factors like diet or storage can really influence the flavor more than the species of egg.
Honestly, to me, quail and chicken eggs pretty much taste the same.  
And, I think blindfolded, most people couldn't tell the difference between species NEARLY as much as they could taste the difference between free range eggs and those from a factory farm/battery raised then held for a month at the grocery store.
I guess the best way I can express it is by way of analogy -- its been hot lately, and I've been getting in the habit of stopping for a bottle of pop on my way home from work.  I have been drinking a lot of orange lately -- sometimes I buy Orange Crush, sometimes Sunkist, sometimes Faygo.  All taste like orange soda, but there are subtle differences between them.