I know nothing about limestone sinks, but I will throw a third alternative in there for you, only because I just had a thread about my new concrete sink and there were comments that it looked like limestone (which was why I opened THIS thread). I know concrete is durable and this might be a good alternative to get a similar look w/o any maintenance issues :)

Hope this isn't a thread hijack :)

it's stone.

to say it the other way around...
it will dissolve very fast because it's made of stone and we all know that stone doesn't hold up very well around water.
it will show plate marks if you leave plates in it for more than a short time.
children will damage it.

I can't imagine a limestone sink even exists, but I guess it could. That being said, just because it does, doesn't mean it should. Limestone may be fine for floors, but it is discouraged for counters and I would say even more so for sinks.

We have French Blue limestone counters in our master bathroom and as tiles in the shower. Very pretty, but the counter needs to be rehoned after the window washers splashed ammonia solution on it. It is definitely reactive, and will be etched by things like lemon juice -- would that bother you? You can seal it, and would in fact have to seal that concrete sink, too. Or you can look for less reactive material and be sanguine.
lynn

I have a limestone floor. It's sealed with Miracle Sealant Porous Plus...2 coats. Everything still stains and etches it, if left on it for more than a minute and a half (well, that's literary hyperbole, but you know what I mean). Fortunately, mine is SO variable to begin with that you can't tell the difference between what God put there and what my messy son or my clumsy self did. But I'd think long and hard about a sink made of limestone.