What are the relative merits of stainless steel vs. granite composite sinks?
Your question verges on asking for opinions rather than a technical answer. The functions of either type are identical. Stainless has always been considered the best choice for longevity and durability. The newer composites are very popular, but somewhat suspectable to scratching from hard metal cookware such as cast iron. I have seen some disclosures on various brands that warn of staining from substances such as wine and dyes. They also warn against the use of certain abrasive cleaning products, so more care must be taken with composites. They are however, very durable, less noisy and can add style to a kitchen decor.

As far as installation under a stone countertop, this is typically not a DIY project. Granite fabricators take great pains to prep the mounting surface. The sink is dry fitted and the cutting and polishing the adjoining edges is done precisely to the individual units. They are then epoxied in place, usually with the counter upside down, clamped and allowed to cure. If done on site, install usually would have to be done from underneath,(unless the slab is small and can be flipped over) not the optimal way and very hard to clamp into place if not impossible. Ordering the counter with the hole precut and polished needs to be EXACT, or you will be in a world of hurt when you go to mate the counter with your sink. My preferred counter fabricator only changes $85 for installing a supplied bowl. I think that is a bargain and the bond is warrantied.