Cost and available mounting space normally dictates which one to use. If I wanted to put 40, 1-circuit boxes hanging off a gutter for a resi panel, I could do that, but it's more compact and more cost effective to use a panelboard.
Group mounted breakers are breakers mounted on a common pan connected to a common vertical bus assembly, examples are breakers in load centers, panelboards and some UL891 Switchboards.
Individually mounted breakers are just that. These are typically found only in switchboard construction. They are mounted on separate assemblies with "runbacks" to the main horizontal bus. Typically individually mounted breakers are breakers rated 1600A and larger in switchboards, however that is not to say that there may not be an occasion for a smaller frame that would be individually mounted. Also, in some cases the breakers may be compartmentalized (barriered) so the breaker is enclosed on all sides.
Take a look at the following, this should help some.