Difficult to respond to this one, as you're attempting to isolate a single element of a wine amongst an endless amount of others.
Are old vines always good? No, of course not. Can they be a major component of how a particular wine tastes? Yes, they can. Or that component can be so manipulated as to be submerged into mediocrity.
And yes, sure, a lot of it is hype. But anyone who has had the fortunate ability to taste a fairly wide array of "old vine" wines has to have noticed different characteristics amongst old and new vine grape style, and the wine that results.
Let's get away from the zinfandel category and look at syrah. Tahbilk, from Nagambie Lakes/Goulburn/Victoria in Australia, has a separate release of old vines syrah they produce. They are undeniably old vines, by anyone's designation or definition, because they were planted back in the 1800s. Each year there is a little bit less release, because each year the vines produce less and less fruit, and more vines succumb to old age and disease. Taste the old vines production next to the more prolific and much younger vines' production, and you can clearly pick out which is which, for they are entirely different creatures.
The old vines are more like trees, with thick, gnarled trunks; they produce very little canopy and very little fruit, but the fruit that does come is incredibly intense and concentrated, and usually makes the same kind of wine.
On one of the vineyards my company owns there is a single hillside vineyard of old vines Petite Sirah, all on its original rootstock too. It is small, looks scraggly, and produces very little fruit, but fruit of that same intensity---such intensity, I might add, that it is used selectively as a blender with other wines from younger vines, because it adds an element missing from those wines. And those of us familiar with the wines can always tell when some of that PS is in a blend, for it is distinctive.
And tagging on what Mark said in his post, I especially love the characteristics that age brings in Mourvedre/Monastrell and Grenache.
Finally, if vines are in any way like people (armchair anthromorphing, anyone?) isn't it almost always the case that maturity in a person brings more depth and complexity? (Mind you, a doddering old man is saying this.

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