Also, which are easier to maintain?
No. Drop in sinks are easier to install.
Everything depends on the brand, but installation of them is a different story. The farm sink usually requires a different kind of cabinet than the undermount sink.
I’m not sure if it’s different for different types of countertop materials, but for Corian solid surface it depends. If it’s a drop-in farmhouse sink, as stated below, then I would think it would only be an additional cost if it needs a special cabinet.
An undermount farmhouse sink versus a standard undermount sink would be more expensive. This is for a Corian countertop, however, because Corian comes 1/2" thick, but the front edge could be built up to, for example, 1 1/2" thick. For a standard undermount sink cutout, the finished cutout for the sink would be 1/2" thick as a standard (unless build up is specially ordered). For an undermount farmhouse sink, because the cutout is next to the front edge that is now 1 1/2" thick, having the cutout be 1/2" thick only would look strange, so we normally build the edge up for the cutout to the same thickness as the front of the countertop.
To help in understanding, as it’s hard to describe, google “undermount sink in Corian” and then google “undermount farmhouse sink in Corian” and compare the pictures. For a quartz or granite material, where they don’t build up the edge and the thickness of the countertop is whatever the material thickness is, I would say it’s probably not much of a difference between the two in cost. For other materials, I’m not sure.
The answer is simply yes.
As a 12 years designer working with all brands and showrooms, I have found that farmhouse sinks will usually be more expensive.
It depends on the brand, of course, for there are undermount sinks that are pricey but on average yes.
As far as installation, farmhouse sink will need a little work around the cabinet and plywood top, but it’s easy enough if you find a reliable company or installer.
Yeah, it does depend on the brand and type of the sink. I’ve recently purchased a new farmhouse sink that was not that expensive
Actually, I anted to say that this sink fits perfectly in my apartment! I thought it would look out of the wall but it fits just right!
Lol, guys I have a small update… The sink I bought was actually a fake one. That is what you get when you buy from a local small store… I couldn’t believe it 
A friend of mine, who is an interior designer, came to my house and told me that I am a loser 'cause I’ve bought not a real farmhouse sink but a sink that looks like it, but at the same price! I was so upset that he decided to make me a present and bought me a great sink himself! I’ve checked some reviews here 10 Best Farmhouse Sink Reviews 2021 - Expert Buying Guide so that from now on I know for sure how a real one looks!