In my experience, the wire mesh kind have always gone ignored. The finches seem to prefer either the socks, or the slit tube feeders, which I have 2 of these days. Here's my take on each:
Mesh feeder: As I said, the con is definately that the birds tend to dislike them, probably due to the fact that the metal is probably not so comfortable to shove their beaks into. They do hold up to squirrels, and also to the environment, and are easy to clean. I tried one once, and now it is a dust collector in the shed. Also, the seed spills out easy in the wind, and when shaken around by the birds.
Slit hole tube feeder: I have 2 of these currently, because they hold up well to the elements, are easy to fill, and keep seed dry. My finches love them, seemingly better then any other style. However, there is a con to these, and that is the perches. The perches on them allow house sparrows to have a seat and eat your expensive niger seed. I've heard of ones with perches on the top of the slits, but I've not tried them.
Thistle socks: I've had many of these over the years, and they do work. I'll start with the pros, and those would be that the finches like them, they keep sparrows off, they are cheap in price, and a lot of birds can use them at once. The cons are that they are a pain in the butt to fill, they get torn up easily if squirrels get to them, they don't last too long, they allow seed to get wet and compacted, and they also get tossed around by the wind, spilling your expensive seed all over the place, and once empty, they proceed to blow away in the wind.
And here's a con to all styles..........The cost of the seed that goes in them.