In general, condenser mics are more sensitive than dynamics, which can be good or bad. They require power, either supplied back up through the mic cable, called "phantom power", usually 48v, or by battery, or from a separate power supply, as in the case of tube mics, where the tube requires more than phantom power can supply. Some condensers are made specifically for live work, usually called "hand held condensers". Condensers (called capacitor mics on the other side of the pond) are often used for live work on softer, more acoustic sources.
The AKG C414 is a great instrument recording mic which is also a standard for stage work with strings and woodwinds in particular.
Dynamic mics are often used in recording as well, especially for drums and guitar cabs, where a less sensitive mic is just fine, and several have been used very successfully for vocals, such as Shure SM-7. There really is no rule of thumb for what mics to use, except that you never know what will sound good on a given source until you listen.
As a rule, however, condensers will generally not work well if you have a lot of background noise, such as traffic, breathing, foot tapping, and catfights outside, and they will be prone to feedback in loud live performance situations. Condensers are rarely used live with loud music, but may be very useful for softer music using acoustic instruments. Almost all studio recording involves a combination of the two. Hope this helps.-Richie