Yes there is a difference in taste between the two 'base liquors' and if you were tasting both straight it would be readily apparent.
However, once you have added the strong flavor of coffee liquer and sweetness and orangey aromatics of triple sec, the difference is far from pronounced.
The subdued apple of the Applejack is even more subdued, though the drink tastes a little sweeter, because of the apple.
I had grape brandy when I first made the drink. When I went to replace it, i thought to go with the Applejack. At this point, I don't know if I have a preference.
If viewed as two different original drinks, I'll need two different names. Hey, how about "nightcapple" for the version made with Laird's?
Mostly unrelated (altho' it is why I bought the Applejack) is the fact that my local has seemingly ceased to restock the brandy section. Two cognacs of unfamiliar makers and one Calvados made up their selection of imports.