The fact that the two tires are different brands would suggest they may have different traction/handling capabilities. One may stick better than another causing one end to break loose sooner than the other. The tires may have different rubber compound and with changing temperatures, one compound may behave differently than another (eg, one gets harder and less sticky at cold temps sooner or may behave differently if driving hard).
You could probably get used to the driving characteristics, but you wouldn't have to worry about any potential differences if it was the same model tire.
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