>>455369The kind of bivy quoted in the OP and
>>455387 is really more of a "bivy tent" than anything. These are designed for high alpine bivouacs, as temporary refuge against the elements.
There are some huge compromises with these shelters, namely space limitations. It's basically like a coffin and not only won't your gear won't fit inside, but when you get in and out of them during a rainstorm, the rain will come right in and get your sleeping bag wet. This may be an acceptable compromise in a few situations: you are camping high above treeline and you expect the winds to be too severe for a tent or tarp shelter, or else you simply want a waterproof shelter that can be set up quickly, with minimal energy output on your part. It's for these reasons that bivy tents only ever make sense for use in serious mountaineering.
For general dispersed camping, in mixed situations, or otherwise for things other than extreme mountaineering, especially if you are concerned about reducing your pack weight, a tarp + a "bivy bag" makes a lot more sense.
The difference between a bivy tent and a bivy bag is that the bag is just that: a fabric cover for your sleeping bag that is waterproof on bottom, breathable on top, and seals up against the bugs. They're actually very easy and affodable to sew yourself, and I'm attaching a picture of one that I put together in about 45 minutes with a cheap sewing machine and some fabric I ordered online (total cost in the $30 range).
A tarp is going to be much more spacious than a bivy tent, and will often end up weighing quite a bit less than the bivy tent, depending on how large of a tarp you buy (8-16 ounces, plus the stakes and guylines). You can keep your gear out of the elements, you can cook and "live" under them, and you can also fit more people than just yourself inside, unlike a bivy tent. The bivy bag only weighs 4-6 ounces, but is a crucial component to the system, as it keeps blown rain off your sleeping bag.