In a case where the parent stocks are *not that different* like any run of the mill US stock, no particular unusual results would be expected.

A few years back I bought an inseminated Carniolan queen and raised queens from them. The resulting colonies were annoyingly aggressive, as compared to the rest. 

It appears that Mendel was one of the first to actually hybridize honey bees:

> Mendel had always wanted to transfer his experiments from plants to animals and began crossbreeding bees around 1871. He successfully produced a hybrid strain of bees by crossing bees from Egypt and South America that produced excellent honey. However, they were so vicious that they stung everybody around for miles and had to be destroyed. Mendel had little success studying hereditary elements in bees, in part because their reproduction was so hard to control.

SOURCE:
http://nmhm.washingtondc.museum/about/newsletter/VOL7_NO4.pdf

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