If it's going to rain on you, then you want some way of keeping the rain off, or you're going to be miserable. The method of keeping the rain off can be a tarp, a tent, or a bivvy sack. If I'm going backpacking in Southern California, and the weather forecast is for clear skies, then I wouldn't bring any of these things.
If I expect mosquitoes to be very thick where I'm camping, then I want a tent. In cold and windy conditions, a tent keeps off the wind. If the ground is muddy and wet, a tent will keep you dry.
A tarp is an excellent ultralight option, especially if you don't expect large amounts of bad weather, but it requires quite a bit of practice to learn to set it up, and every location is different. When it's windy, tarps tend to flap all night and make noise. If the ground is wet, you'll also want a ground tarp, although this can be a very lightweight piece of plastic.
A bivvy sack is a good option if you're mountaineering and you want a life-saving way of keeping rain and snow off in case of an emergency bivouac, but you don't want to carry a tent. People I know who have slept in bivvy sacks have generally never said anything good about the experience. Moisture tends to condense inside the bivvy sack from your own breath and perspiration, so you end up wet. If it's raining, then rain tends to get on your head no matter what you do.
In the relatively dry conditions here in California, I generally use a down bag and bring a tarp along in case of rain. Once in a while, when I've camped near a creek or in foggy weather, I've woken up in the morning to find the bag damp on the outside from condensation. This is not a huge problem. The bag will still retain its insulating ability when the only moisture on it is this type of condensation.
Down sleeping bags are much lighter and smaller than synthetic ones for the same amount of insulation. The main reason for using a synthetic bag is if you can't afford a down one.