I hope I'm right because you asked an intriguing question and I didn't want to hijack rslindsa's thread with an answer.
Well, I'm not a professional nor an "expert", but here's my opinion.
The wine from an area is affected by the soil, weather conditions, available water, the age of the vines, how it is picked, how it is made, I could go on, but I'm sure you get the idea.
You're probably aware that a happy grape vine produces really crappy wine. The vine needs to be stressed in order to render a grape with enough flavor concentration to make a good wine.
The Old World: Ancient grapes with very deep roots planted in limestony or chalky soil will produce wine with a wonderful minerality. There's a wine I really like from the Vacqueryas region of France, called "le Sang des Cailloux." -- literally "Blood of the Stones." You can tell they're proud of their minerals.
Combine that with hand picking techniques that pull only the ripe grapes, careful aging in French Oak, and generally a craftsmanship style to winemaking that allows for the wine to develop over a long time, really does give a complexity of mouthfeel and aftertaste that you noted in your post.
Compare that to the "New World". Younger grape vines that have not had as much time to develop the rootstock. Larger expanses of plantings that lend themselves to picking by machinery. Machine picking means you get not only the ripest grapes, but also the unripe grapes, plus whatever bugs, lizards and snakes that weren't quick enough to get out of the way. If you think I'm exaggerating about that, think again. Everything gets dumped into the crusher. There's no one assigned to pick out the lizards.
Then there are the cultural differences. Australians and Californians tend to like their wine very fruity. It can be dry or sweet - but fruit forward is the taste that appeals. Fruit forward wines tend to have that one-note taste that you mentioned. It's the tobacco, leather, spicy, and minerally tastes that tend to give a wine its complexity and allow for a strong and multi-textured finish.
Not all "New World" wine has that one note taste with no complexity. But you really have to go to some of the more boutique wineries and those with smaller production to match the complexity of wines from the European nations.
I don't have the opinion that one is better or worse than the other. It has a lot to do with cultural differences and what you're used to drinking. I live in a wine producing region of California. I really enjoy a lot of our local wines. Wines that are fruit forward and show really big right after bottling. But I tend to savor the wines from the Rhone region a bit more. And lately I try to seek out some of the finer local producers for wines of complexity. Our area does better for Pinot Noir and Chardonnay in this regard. Although I've had Rousannes from local grapes that are truly wonderful and give you a LOT to talk about trying to describe their flavors.