I prefer the open CFLs (mostly because I haven't tried the closed type and am resistant to change), but I can certainly see merit in the closed type. They generally have a soft white enclosure around the fluorescent tubing to make it look more like a traditional round bulb. Enclosed CFLs very closely resemble frosted incandescent bulbs, which is a bonus for those who have distaste for the odd "swirly" look of open compact fluorescent light bulbs.
You'll get the closest aesthetic match to incandescents with enclosed CFLs around the 10-13 watt zone; higher watt compact fluorescents are bigger and start to look more like globe incandescents. You can use enclosed CFLs everywhere you use open CFLs or incandescents for a more traditional look to your light fixtures.
Cold cathode compact fluorescents
are usually covered by a clear enclosure, but they're not the same as standard covered CFLs. Cold cathode CFLs have a lot of advantages over standard compact fluorescents; they start instantly in temperatures as low as -10 F and continue operating in that temperature, they're dimmable, and are generally more sturdy. They're fairly expensive compared to standard CFLs, and as such are not available in very high wattage, but they're excellent special application bulbs especially if you need energy efficient lighting outside.
I'll probably try some enclosed compact fluorescent light bulbs at some point, but for now I'll stay with my trusty TCP daylight bulbs
. They've served me well for over five years now; the annoyance of bulbs burning out and suddenly being plunged into darkness is far removed from memory, and it can be for you too if you pick up some compact fluorescent light bulbs to replace your incandescents.