The short version
Concrete pavers cost less, are dimensionally consistent, come in more patterns, and are far easier to lift and reset if something ever has to be dug up underneath them. Natural bluestone costs more, is quarried in this region so it looks like it belongs, and every piece is slightly different — which is the whole appeal and also the reason it takes longer to lay well.
Both, installed properly, will outlast the base under them. Neither is a solution to a bad base.
How each one handles a Hudson Valley winter
This is the question that actually matters here, and the answer is mostly about water rather than about the material.
Concrete pavers are manufactured dense and are dimensionally stable through freeze-thaw. Their vulnerability is de-icing salt on the surface and joint sand washing out of the joints, both of which are maintenance rather than failure. Because they interlock and flex slightly as a system, a paver field tolerates minor base movement without cracking.
Bluestone is a dense sedimentary stone and stands up well, but it is laid as individual pieces — either dry on a bedding course or wet-set in mortar on a concrete slab. Wet-set bluestone is the one to think about carefully in this climate: if water gets under the stone and freezes, it pushes individual pieces loose, and the repair is a mortar repair rather than a lift-and-reset.
If a patio is going to be salted every winter — a north-facing entry, a set of steps — that is worth saying to whoever is quoting it, because it changes what to specify.
Repairs, which nobody thinks about until they need one
This is where pavers win decisively and it is the argument most people have not heard. Pavers are dry-laid on a bedding course, so if a utility line has to be reached, a drain added, or a section settles, that area is lifted, the work is done, and the same pavers go back down. Done well, the repair is invisible.
Dry-laid natural stone can be lifted the same way. Mortared stone on a slab cannot: reaching what is underneath means breaking it out, and matching a mortar joint colour on a patio that has weathered for five years is difficult to do invisibly.
So which one
Choose pavers if budget is a real constraint, if anything is likely to be dug up in future, if you want a large area covered consistently, or if you want a specific pattern.
Choose bluestone if the look matters more than the difference in cost, if the house is old enough that manufactured concrete would look wrong against it, or if you simply want the material that this part of New York has been building with for two hundred years.
What we would not do is choose either one and then economise on the base to afford it. A cheaper stone on a proper base is a patio. A better stone on a thin base is a repair job with a date on it.