Not a huge, huge bourbon fan, but Buffalo Trace used to be a solid "budget" option during my trendy cocktail phase. Perfectly passable, even enjoyable, straight.
Oak contains vanillins and wood sugars. French oak tends to taste a little bit more spiced and American oak tends to be a bit more sweet.
When making my apple mead, I always add French oak while maturing, and it makes a huge difference in taste. I add it mostly for the tannins though (the bitter part of tea), which gives it more "chew" (like the difference between white and red wine).